%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT159+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 : n016.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 05:06:07 PM UTC 2026
% Result : Theorem 5.34s 5.73s
% Output : CNFRefutation 40.07s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 1072)
% Comments :
%------------------------------------------------------------------------------
fof(fact_pigeonhole,axiom,
! [X4,X2,X5,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(X6,c_Set_Oimage(X5,X6,X2,X4)),c_Finite__Set_Ocard(X5,X4))
=> ~ c_Fun_Oinj__on(X5,X6,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
fof(fact_setsum__cl__ivl__Suc,axiom,
! [X2,X34,X29,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),X34)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))) = c_Groups_Ozero__class_Ozero(X6) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),X34)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))) = c_Groups_Oplus__class_Oplus(X6,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X29)),hAPP(X2,hAPP(c_Nat_OSuc,X29))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cl__ivl__Suc) ).
fof(fact_setsum__op__ivl__Suc,axiom,
! [X2,X34,X29,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X34)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))) = c_Groups_Ozero__class_Ozero(X6) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X34)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))) = c_Groups_Oplus__class_Oplus(X6,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,X29)),hAPP(X2,X29)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).
fof(fact_setsum__insert,axiom,
! [X2,X13,X12,X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( c_Finite__Set_Ofinite(X6,X12)
=> ( ~ c_member(X6,X13,X12)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X2,c_Set_Oinsert(X6,X13,X12)) = c_Groups_Oplus__class_Oplus(X5,hAPP(X2,X13),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X2,X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__insert) ).
fof(fact_setsum_Oinsert,axiom,
! [X1,X8,X4,X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( c_Finite__Set_Ofinite(X6,X4)
=> ( ~ c_member(X6,X8,X4)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X1,c_Set_Oinsert(X6,X8,X4)) = c_Groups_Oplus__class_Oplus(X5,hAPP(X1,X8),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X1,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert) ).
fof(fact_atLeastatMost__psubset__iff,axiom,
! [X44,X26,X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14),c_SetInterval_Oord__class_OatLeastAtMost(X6,X26,X44))
<=> ( ( ~ c_Orderings_Oord__class_Oless__eq(X6,X13,X14)
| ( c_Orderings_Oord__class_Oless__eq(X6,X26,X13)
& c_Orderings_Oord__class_Oless__eq(X6,X14,X44)
& ( c_Orderings_Oord__class_Oless(X6,X26,X13)
| c_Orderings_Oord__class_Oless(X6,X14,X44) ) ) )
& c_Orderings_Oord__class_Oless__eq(X6,X26,X44) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
fof(fact_atLeastatMost__subset__iff,axiom,
! [X44,X26,X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14),c_SetInterval_Oord__class_OatLeastAtMost(X6,X26,X44))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X13,X14)
| ( c_Orderings_Oord__class_Oless__eq(X6,X26,X13)
& c_Orderings_Oord__class_Oless__eq(X6,X14,X44) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__subset__iff) ).
fof(fact_card__Suc__eq,axiom,
! [X45,X4,X6] :
( c_Finite__Set_Ocard(X6,X4) = hAPP(c_Nat_OSuc,X45)
<=> ? [X64,X65] :
( X4 = c_Set_Oinsert(X6,X64,X65)
& ~ c_member(X6,X64,X65)
& c_Finite__Set_Ocard(X6,X65) = X45
& ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X65 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__eq) ).
fof(fact_ex__least__nat__less,axiom,
! [X29,X21] :
( ~ hBOOL(hAPP(X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X21,X29))
=> ? [X55] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X29)
& ! [X62] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62,X55)
=> ~ hBOOL(hAPP(X21,X62)) )
& hBOOL(hAPP(X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_subset__insert,axiom,
! [X7,X4,X8,X6] :
( ~ c_member(X6,X8,X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oinsert(X6,X8,X7))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
fof(fact_folding__one_Oinsert,axiom,
! [X8,X4,X12,X2,X6] :
( c_Finite__Set_Ofolding__one(X6,X2,X12)
=> ( c_Finite__Set_Ofinite(X6,X4)
=> ( ~ c_member(X6,X8,X4)
=> ( X4 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> hAPP(X12,c_Set_Oinsert(X6,X8,X4)) = hAPP(hAPP(X2,X8),hAPP(X12,X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).
fof(fact_atLeastLessThanSuc,axiom,
! [X29,X34] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
=> c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29)) = c_Set_Oinsert(tc_Nat_Onat,X29,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,X29)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
=> c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc) ).
fof(fact_add__leE,axiom,
! [X25,X39,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X39),X25)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X6,X5] :
( class_Orderings_Oord(X5)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,X5),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X5),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X5),X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_insert__ident,axiom,
! [X7,X4,X8,X6] :
( ~ c_member(X6,X8,X4)
=> ( ~ c_member(X6,X8,X7)
=> ( c_Set_Oinsert(X6,X8,X4) = c_Set_Oinsert(X6,X8,X7)
<=> X4 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(fact_card_Oinsert,axiom,
! [X8,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( ~ c_member(X6,X8,X4)
=> c_Finite__Set_Ocard(X6,c_Set_Oinsert(X6,X8,X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(X6,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).
fof(fact_setsum__infinite,axiom,
! [X2,X4,X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( ~ c_Finite__Set_Ofinite(X6,X4)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X2,X4) = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__infinite) ).
fof(fact_setsum_Oinfinite,axiom,
! [X1,X4,X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( ~ c_Finite__Set_Ofinite(X6,X4)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X1,X4) = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinfinite) ).
fof(fact_insertCI,axiom,
! [X14,X7,X13,X6] :
( ( ~ c_member(X6,X13,X7)
=> X13 = X14 )
=> c_member(X6,X13,c_Set_Oinsert(X6,X14,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
fof(fact_not__add__less1,axiom,
! [X40,X41] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X40),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X41,X40] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_card__insert__if,axiom,
! [X8,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( ( c_member(X6,X8,X4)
=> c_Finite__Set_Ocard(X6,c_Set_Oinsert(X6,X8,X4)) = c_Finite__Set_Ocard(X6,X4) )
& ( ~ c_member(X6,X8,X4)
=> c_Finite__Set_Ocard(X6,c_Set_Oinsert(X6,X8,X4)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X6,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).
fof(fact_card__insert__disjoint,axiom,
! [X8,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( ~ c_member(X6,X8,X4)
=> c_Finite__Set_Ocard(X6,c_Set_Oinsert(X6,X8,X4)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X6,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
fof(fact_atLeastatMost__empty__iff2,axiom,
! [X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14)
<=> ~ c_Orderings_Oord__class_Oless__eq(X6,X13,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff2) ).
fof(fact_atLeastLessThan__empty__iff2,axiom,
! [X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X13,X14)
<=> ~ c_Orderings_Oord__class_Oless(X6,X13,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
fof(fact_atLeastatMost__empty__iff,axiom,
! [X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ~ c_Orderings_Oord__class_Oless__eq(X6,X13,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff) ).
fof(fact_atLeastLessThan__empty__iff,axiom,
! [X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X6,X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ~ c_Orderings_Oord__class_Oless(X6,X13,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
fof(fact_not__less__eq__eq,axiom,
! [X29,X34] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X29,X34] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,hAPP(c_Nat_OSuc,X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_not__psubset__empty,axiom,
! [X4,X6] : ~ c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
fof(fact_less__le__not__le,axiom,
! [X9,X8,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X9,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_le__SucE,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X25))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25)
=> X35 = hAPP(c_Nat_OSuc,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> X8 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X19,X18,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X18,X19)
=> ~ c_Orderings_Oord__class_Oless(X6,X19,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> ( c_Orderings_Oord__class_Oless(X6,X9,X8)
| X8 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_leD,axiom,
! [X16,X17,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X17,X16)
=> ~ c_Orderings_Oord__class_Oless(X6,X16,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__less,axiom,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> c_Orderings_Oord__class_Oless__eq(X6,X9,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
<=> c_Orderings_Oord__class_Oless(X6,X9,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_order__less__asym,axiom,
! [X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> ~ c_Orderings_Oord__class_Oless(X6,X17,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X18,X19,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X19,X18)
=> ~ c_Orderings_Oord__class_Oless(X6,X18,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> ~ c_Orderings_Oord__class_Oless(X6,X17,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> ~ c_Orderings_Oord__class_Oless(X6,X17,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_less__SucE,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X25))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25)
=> X35 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_less__antisym,axiom,
! [X35,X25] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X35)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,hAPP(c_Nat_OSuc,X35))
=> X35 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X34,X29] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X34)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,hAPP(c_Nat_OSuc,X34))
<=> X29 = X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_empty__iff,axiom,
! [X26,X6] : ~ c_member(X6,X26,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
fof(fact_emptyE,axiom,
! [X13,X6] : ~ c_member(X6,X13,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X8,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
<=> X8 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_equals0D,axiom,
! [X13,X6,X4] :
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> ~ c_member(X6,X13,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
fof(fact_all__not__in__conv,axiom,
! [X4,X6] :
( ! [X3] : ~ c_member(X6,X3,X4)
<=> X4 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X25] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X25),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X17,X16,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( X16 != X17
=> ( ~ c_Orderings_Oord__class_Oless(X6,X16,X17)
=> c_Orderings_Oord__class_Oless(X6,X17,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__cases,axiom,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X16,X17)
=> ( X16 != X17
=> c_Orderings_Oord__class_Oless(X6,X17,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( X16 != X17
=> ( ~ c_Orderings_Oord__class_Oless(X6,X16,X17)
=> c_Orderings_Oord__class_Oless(X6,X17,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X8,X9,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X9,X8)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> X8 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_not__leE,axiom,
! [X16,X17,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X17,X16)
=> c_Orderings_Oord__class_Oless(X6,X16,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X16,X17)
=> c_Orderings_Oord__class_Oless__eq(X6,X17,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_linorder__le__cases,axiom,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X16,X17)
=> c_Orderings_Oord__class_Oless__eq(X6,X17,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_not__one__less__zero,axiom,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_not__one__le__zero,axiom,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_linorder__neqE__nat,axiom,
! [X17,X16] :
( X16 != X17
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_order__less__irrefl,axiom,
! [X16,X6] :
( class_Orderings_Opreorder(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,X16,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_not__less0,axiom,
! [X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__nat__zero__code,axiom,
! [X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_less__zeroE,axiom,
! [X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__irrefl__nat,axiom,
! [X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_equalityE,axiom,
! [X6,X7,X4] :
( X4 = X7
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
fof(fact_card__eq__0__iff,axiom,
! [X4,X6] :
( c_Finite__Set_Ocard(X6,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X6,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
fof(help_c__fequal__1,axiom,
! [X9,X8] :
( ~ hBOOL(hAPP(c_fequal(X8),X9))
| X8 = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_card__infinite,axiom,
! [X4,X6] :
( ~ c_Finite__Set_Ofinite(X6,X4)
=> c_Finite__Set_Ocard(X6,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
fof(fact_setsum__reindex__cong,axiom,
! [X11,X1,X7,X4,X2,X5,X6,X60] :
( class_Groups_Ocomm__monoid__add(X60)
=> ( c_Fun_Oinj__on(X6,X5,X2,X4)
=> ( X7 = c_Set_Oimage(X6,X5,X2,X4)
=> ( ! [X61] :
( c_member(X6,X61,X4)
=> hAPP(X1,X61) = hAPP(X11,hAPP(X2,X61)) )
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X60,X11,X7) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X60,X1,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__cong) ).
fof(fact_setsum__ivl__cong,axiom,
! [X1,X2,X44,X14,X26,X13,X6,X5] :
( ( class_Groups_Ocomm__monoid__add(X5)
& class_Orderings_Oord(X6) )
=> ( X13 = X26
=> ( X14 = X44
=> ( ! [X3] :
( c_Orderings_Oord__class_Oless__eq(X6,X26,X3)
=> ( c_Orderings_Oord__class_Oless(X6,X3,X44)
=> hAPP(X2,X3) = hAPP(X1,X3) ) )
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(X6,X13,X14)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X1,c_SetInterval_Oord__class_OatLeastLessThan(X6,X26,X44)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ivl__cong) ).
fof(fact_folding__one__idem_Ohom__commute,axiom,
! [X38,X11,X12,X2,X6] :
( c_Finite__Set_Ofolding__one__idem(X6,X2,X12)
=> ( ! [X3,X15] : hAPP(X11,hAPP(hAPP(X2,X3),X15)) = hAPP(hAPP(X2,hAPP(X11,X3)),hAPP(X11,X15))
=> ( c_Finite__Set_Ofinite(X6,X38)
=> ( X38 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> hAPP(X11,hAPP(X12,X38)) = hAPP(X12,c_Set_Oimage(X6,X6,X11,X38)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
fof(fact_setsum__strict__mono,axiom,
! [X1,X2,X4,X6,X5] :
( ( class_Groups_Ocomm__monoid__add(X5)
& class_Groups_Oordered__cancel__ab__semigroup__add(X5) )
=> ( c_Finite__Set_Ofinite(X6,X4)
=> ( X4 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> ( ! [X3] :
( c_member(X6,X3,X4)
=> c_Orderings_Oord__class_Oless(X5,hAPP(X2,X3),hAPP(X1,X3)) )
=> c_Orderings_Oord__class_Oless(X5,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X2,X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X1,X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__strict__mono) ).
fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
! [X7,X4,X12,X1,X42,X2,X5,X6] :
( c_Finite__Set_Ofolding__image__simple__idem(X6,X5,X2,X42,X1,X12)
=> ( c_Finite__Set_Ofinite(X5,X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X4)
=> hAPP(hAPP(X2,hAPP(X12,X7)),hAPP(X12,X4)) = hAPP(X12,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
! [X8,X4,X12,X1,X42,X2,X5,X6] :
( c_Finite__Set_Ofolding__image__simple__idem(X6,X5,X2,X42,X1,X12)
=> ( c_Finite__Set_Ofinite(X5,X4)
=> hAPP(X12,c_Set_Oinsert(X5,X8,X4)) = hAPP(hAPP(X2,hAPP(X1,X8)),hAPP(X12,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
fof(fact_folding__image__simple__idem_Oin__idem,axiom,
! [X8,X4,X12,X1,X42,X2,X5,X6] :
( c_Finite__Set_Ofolding__image__simple__idem(X6,X5,X2,X42,X1,X12)
=> ( c_Finite__Set_Ofinite(X5,X4)
=> ( c_member(X5,X8,X4)
=> hAPP(hAPP(X2,hAPP(X1,X8)),hAPP(X12,X4)) = hAPP(X12,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [X8,X12,X1,X42,X2,X5,X6] :
( c_Finite__Set_Ofolding__image__simple__idem(X6,X5,X2,X42,X1,X12)
=> hAPP(hAPP(X2,X8),X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
fof(fact_ord_OatLeastLessThan__iff,axiom,
! [X31,X32,X48,X46,X47,X6] :
( c_member(X6,X47,c_SetInterval_Oord_OatLeastLessThan(X6,X46,X48,X32,X31))
<=> ( hBOOL(hAPP(hAPP(X46,X32),X47))
& hBOOL(hAPP(hAPP(X48,X47),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
fof(fact_ord_OgreaterThanAtMost__iff,axiom,
! [X31,X32,X48,X46,X47,X6] :
( c_member(X6,X47,c_SetInterval_Oord_OgreaterThanAtMost(X6,X46,X48,X32,X31))
<=> ( hBOOL(hAPP(hAPP(X48,X32),X47))
& hBOOL(hAPP(hAPP(X46,X47),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
fof(fact_range__ex1__eq,axiom,
! [X14,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> ( c_member(X5,X14,c_Set_Oimage(X6,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))))
<=> ? [X3] :
( X14 = hAPP(X2,X3)
& ! [X15] :
( X14 = hAPP(X2,X15)
=> X15 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_subset__image__iff,axiom,
! [X4,X2,X5,X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,c_Set_Oimage(X5,X6,X2,X4))
<=> ? [X43] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X43,X4)
& X7 = c_Set_Oimage(X5,X6,X2,X43) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X6,X5] :
( class_Orderings_Oord(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X5),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X5,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_setsum__ub__add__nat,axiom,
! [X59,X2,X29,X34,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X59))) = c_Groups_Oplus__class_Oplus(X6,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X29)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X59)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ub__add__nat) ).
fof(fact_card__bij__eq,axiom,
! [X1,X7,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X6,X5,X2,X4),X7)
=> ( c_Fun_Oinj__on(X5,X6,X1,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Set_Oimage(X5,X6,X1,X7),X4)
=> ( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Finite__Set_Ofinite(X5,X7)
=> c_Finite__Set_Ocard(X6,X4) = c_Finite__Set_Ocard(X5,X7) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
fof(fact_the__inv__into__into,axiom,
! [X7,X8,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> ( c_member(X5,X8,c_Set_Oimage(X6,X5,X2,X4))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_member(X6,hAPP(c_Fun_Othe__inv__into(X6,X5,X4,X2),X8),X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
fof(fact_f__the__inv__into__f,axiom,
! [X9,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> ( c_member(X5,X9,c_Set_Oimage(X6,X5,X2,X4))
=> hAPP(X2,hAPP(c_Fun_Othe__inv__into(X6,X5,X4,X2),X9)) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
fof(fact_inj__image__subset__iff,axiom,
! [X7,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X6,X5,X2,X4),c_Set_Oimage(X6,X5,X2,X7))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
fof(fact_inj__on__iff__surj,axiom,
! [X27,X5,X6,X4] :
( X4 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> ( ? [X24] :
( c_Fun_Oinj__on(X6,X5,X24,X4)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X6,X5,X24,X4),X27) )
<=> ? [X28] : c_Set_Oimage(X5,X6,X28,X27) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
fof(fact_setsum__add__nat__ivl,axiom,
! [X2,X59,X29,X34,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X59)
=> c_Groups_Oplus__class_Oplus(X6,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,X29)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X29,X59))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,X59)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).
fof(fact_inj__on__iff__card__le,axiom,
! [X7,X5,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Finite__Set_Ofinite(X5,X7)
=> ( ? [X24] :
( c_Fun_Oinj__on(X6,X5,X24,X4)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X6,X5,X24,X4),X7) )
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X5,X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_the__inv__into__onto,axiom,
! [X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> c_Set_Oimage(X5,X6,c_Fun_Othe__inv__into(X6,X5,X4,X2),c_Set_Oimage(X6,X5,X2,X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
fof(fact_inj__on__the__inv__into,axiom,
! [X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> c_Fun_Oinj__on(X5,X6,c_Fun_Othe__inv__into(X6,X5,X4,X2),c_Set_Oimage(X6,X5,X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
fof(fact_inj__on__strict__subset,axiom,
! [X4,X7,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X7)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X6,X5,X2,X4),c_Set_Oimage(X6,X5,X2,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_endo__inj__surj,axiom,
! [X2,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Set_Oimage(X6,X6,X2,X4),X4)
=> ( c_Fun_Oinj__on(X6,X6,X2,X4)
=> c_Set_Oimage(X6,X6,X2,X4) = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
fof(fact_setsum__SucD,axiom,
! [X29,X4,X2,X6] :
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat,X2,X4) = hAPP(c_Nat_OSuc,X29)
=> ? [X3] :
( c_member(X6,X3,X4)
& 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_inj__image__mem__iff,axiom,
! [X4,X13,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> ( c_member(X5,hAPP(X2,X13),c_Set_Oimage(X6,X5,X2,X4))
<=> c_member(X6,X13,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_card__inj__on__le,axiom,
! [X7,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X6,X5,X2,X4),X7)
=> ( c_Finite__Set_Ofinite(X5,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X5,X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_image__iff,axiom,
! [X4,X2,X5,X42,X6] :
( c_member(X6,X42,c_Set_Oimage(X5,X6,X2,X4))
<=> ? [X3] :
( c_member(X5,X3,X4)
& X42 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_card_Oremove,axiom,
! [X8,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_member(X6,X8,X4)
=> c_Finite__Set_Ocard(X6,X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(X6,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oinsert(X6,X8,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oremove) ).
fof(fact_setsum__head__Suc,axiom,
! [X2,X29,X34,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X29)) = c_Groups_Oplus__class_Oplus(X6,hAPP(X2,X34),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34),X29))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__Suc) ).
fof(fact_setsum__head__upt__Suc,axiom,
! [X2,X29,X34,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,X29)) = c_Groups_Oplus__class_Oplus(X6,hAPP(X2,X34),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34),X29))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).
fof(fact_inj__on__def,axiom,
! [X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
<=> ! [X3] :
( c_member(X6,X3,X4)
=> ! [X10] :
( c_member(X6,X10,X4)
=> ( hAPP(X2,X3) = hAPP(X2,X10)
=> X3 = X10 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_inj__image__eq__iff,axiom,
! [X7,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> ( c_Set_Oimage(X6,X5,X2,X4) = c_Set_Oimage(X6,X5,X2,X7)
<=> X4 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_setsum__eq__Suc0__iff,axiom,
! [X2,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat,X2,X4) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ? [X3] :
( c_member(X6,X3,X4)
& hAPP(X2,X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& ! [X10] :
( c_member(X6,X10,X4)
=> ( X3 != X10
=> hAPP(X2,X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
fof(fact_finite__imageD,axiom,
! [X4,X2,X5,X6] :
( c_Finite__Set_Ofinite(X6,c_Set_Oimage(X5,X6,X2,X4))
=> ( c_Fun_Oinj__on(X5,X6,X2,X4)
=> c_Finite__Set_Ofinite(X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(fact_image__mono,axiom,
! [X2,X5,X7,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X6,X5,X2,X4),c_Set_Oimage(X6,X5,X2,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_setsum__eq__1__iff,axiom,
! [X2,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat,X2,X4) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ? [X3] :
( c_member(X6,X3,X4)
& hAPP(X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& ! [X10] :
( c_member(X6,X10,X4)
=> ( X3 != X10
=> hAPP(X2,X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).
fof(conj_0,hypothesis,
! [X68] :
( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X68,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
=> ( c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X68,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))
=> v_thesis____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_finite__surj__inj,axiom,
! [X2,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oimage(X6,X6,X2,X4))
=> c_Fun_Oinj__on(X6,X6,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_card__image__le,axiom,
! [X2,X5,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,c_Set_Oimage(X6,X5,X2,X4)),c_Finite__Set_Ocard(X6,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
fof(fact_the__inv__f__f,axiom,
! [X8,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> hAPP(c_Fun_Othe__inv__into(X6,X5,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)),X2),hAPP(X2,X8)) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__f__f) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [X2,X5,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Finite__Set_Ocard(X5,c_Set_Oimage(X6,X5,X2,X4)) = c_Finite__Set_Ocard(X6,X4)
=> c_Fun_Oinj__on(X6,X5,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [X2,X5,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Fun_Oinj__on(X6,X5,X2,X4)
<=> c_Finite__Set_Ocard(X5,c_Set_Oimage(X6,X5,X2,X4)) = c_Finite__Set_Ocard(X6,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_the__inv__into__f__f,axiom,
! [X8,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> ( c_member(X6,X8,X4)
=> hAPP(c_Fun_Othe__inv__into(X6,X5,X4,X2),hAPP(X2,X8)) = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
fof(fact_the__inv__into__f__eq,axiom,
! [X9,X8,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> ( hAPP(X2,X8) = X9
=> ( c_member(X6,X8,X4)
=> hAPP(c_Fun_Othe__inv__into(X6,X5,X4,X2),X9) = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
fof(fact_subset__card__intvl__is__intvl,axiom,
! [X45,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,c_Finite__Set_Ocard(tc_Nat_Onat,X4))))
=> X4 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,c_Finite__Set_Ocard(tc_Nat_Onat,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
fof(fact_ord_OgreaterThanLessThan__iff,axiom,
! [X31,X32,X48,X47,X6] :
( c_member(X6,X47,c_SetInterval_Oord_OgreaterThanLessThan(X6,X48,X32,X31))
<=> ( hBOOL(hAPP(hAPP(X48,X32),X47))
& hBOOL(hAPP(hAPP(X48,X47),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
fof(fact_ord_OatLeastAtMost__iff,axiom,
! [X31,X32,X46,X47,X6] :
( c_member(X6,X47,c_SetInterval_Oord_OatLeastAtMost(X6,X46,X32,X31))
<=> ( hBOOL(hAPP(hAPP(X46,X32),X47))
& hBOOL(hAPP(hAPP(X46,X47),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
fof(fact_finite__surj,axiom,
! [X2,X7,X5,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,c_Set_Oimage(X6,X5,X2,X4))
=> c_Finite__Set_Ofinite(X5,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
fof(fact_image__insert,axiom,
! [X7,X13,X2,X6,X5] : c_Set_Oimage(X5,X6,X2,c_Set_Oinsert(X5,X13,X7)) = c_Set_Oinsert(X6,hAPP(X2,X13),c_Set_Oimage(X5,X6,X2,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
fof(fact_finite__UNIV__surj__inj,axiom,
! [X2,X6] :
( c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> ( c_Set_Oimage(X6,X6,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))
=> c_Fun_Oinj__on(X6,X6,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_card__image,axiom,
! [X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> c_Finite__Set_Ocard(X5,c_Set_Oimage(X6,X5,X2,X4)) = c_Finite__Set_Ocard(X6,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
fof(fact_insert__image,axiom,
! [X2,X5,X4,X8,X6] :
( c_member(X6,X8,X4)
=> c_Set_Oinsert(X5,hAPP(X2,X8),c_Set_Oimage(X6,X5,X2,X4)) = c_Set_Oimage(X6,X5,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [X2,X6] :
( c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(X6,X6,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> c_Set_Oimage(X6,X6,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_finite__Plus__iff,axiom,
! [X7,X4,X5,X6] :
( c_Finite__Set_Ofinite(tc_sum(X6,X5),c_Sum__Type_OPlus(X6,X5,X4,X7))
<=> ( c_Finite__Set_Ofinite(X6,X4)
& c_Finite__Set_Ofinite(X5,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [X7,X4,X5,X6] :
( c_Finite__Set_Ofinite(tc_sum(X6,X5),c_Sum__Type_OPlus(X6,X5,X4,X7))
=> c_Finite__Set_Ofinite(X6,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
fof(fact_finite__PlusD_I2_J,axiom,
! [X7,X4,X5,X6] :
( c_Finite__Set_Ofinite(tc_sum(X6,X5),c_Sum__Type_OPlus(X6,X5,X4,X7))
=> c_Finite__Set_Ofinite(X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_doubleton__eq__iff,axiom,
! [X44,X26,X14,X13,X6] :
( c_Set_Oinsert(X6,X13,c_Set_Oinsert(X6,X14,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))) = c_Set_Oinsert(X6,X26,c_Set_Oinsert(X6,X44,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))))
<=> ( ( X13 = X26
& X14 = X44 )
| ( X13 = X44
& X14 = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
! [X45,X2,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> ( hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X6)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X45)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).
fof(fact_Ints__odd__less__0,axiom,
! [X13,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_member(X6,X13,c_Int_Oring__1__class_OInts(X6))
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,c_Groups_Oone__class_Oone(X6),X13),X13),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless(X6,X13,c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
fof(fact_setsum__shift__lb__Suc0__0,axiom,
! [X45,X2] :
( hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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)),X45)) = 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),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).
fof(fact_subset__inj__on,axiom,
! [X4,X7,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_Fun_Oinj__on(X6,X5,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
fof(fact_card__Plus,axiom,
! [X7,X5,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Finite__Set_Ofinite(X5,X7)
=> c_Finite__Set_Ocard(tc_sum(X6,X5),c_Sum__Type_OPlus(X6,X5,X4,X7)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X5,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
fof(fact_card__Plus__conv__if,axiom,
! [X7,X5,X4,X6] :
( ( ( c_Finite__Set_Ofinite(X6,X4)
& c_Finite__Set_Ofinite(X5,X7) )
=> c_Finite__Set_Ocard(tc_sum(X6,X5),c_Sum__Type_OPlus(X6,X5,X4,X7)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X5,X7)) )
& ( ~ ( c_Finite__Set_Ofinite(X6,X4)
& c_Finite__Set_Ofinite(X5,X7) )
=> c_Finite__Set_Ocard(tc_sum(X6,X5),c_Sum__Type_OPlus(X6,X5,X4,X7)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
fof(fact_rangeI,axiom,
! [X5,X8,X2,X6] : c_member(X6,hAPP(X2,X8),c_Set_Oimage(X5,X6,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_range__eqI,axiom,
! [X5,X6,X8,X2,X14] :
( X14 = hAPP(X2,X8)
=> c_member(X6,X14,c_Set_Oimage(X5,X6,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_imageI,axiom,
! [X2,X5,X4,X8,X6] :
( c_member(X6,X8,X4)
=> c_member(X5,hAPP(X2,X8),c_Set_Oimage(X6,X5,X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact_image__eqI,axiom,
! [X6,X4,X5,X8,X2,X14] :
( X14 = hAPP(X2,X8)
=> ( c_member(X5,X8,X4)
=> c_member(X6,X14,c_Set_Oimage(X5,X6,X2,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X5,X2,X14,X4,X8,X6] :
( c_member(X6,X8,X4)
=> ( X14 = hAPP(X2,X8)
=> c_member(X5,X14,c_Set_Oimage(X6,X5,X2,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_inj__on__iff,axiom,
! [X9,X8,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> ( c_member(X6,X8,X4)
=> ( c_member(X6,X9,X4)
=> ( hAPP(X2,X8) = hAPP(X2,X9)
<=> X8 = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__onD,axiom,
! [X9,X8,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> ( hAPP(X2,X8) = hAPP(X2,X9)
=> ( c_member(X6,X8,X4)
=> ( c_member(X6,X9,X4)
=> X8 = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
fof(fact_inj__on__contraD,axiom,
! [X9,X8,X4,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,X4)
=> ( X8 != X9
=> ( c_member(X6,X8,X4)
=> ( c_member(X6,X9,X4)
=> hAPP(X2,X8) != hAPP(X2,X9) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_subset__singletonD,axiom,
! [X8,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oinsert(X6,X8,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))))
=> ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
| X4 = c_Set_Oinsert(X6,X8,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
fof(fact_finite__Plus,axiom,
! [X7,X5,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( c_Finite__Set_Ofinite(X5,X7)
=> c_Finite__Set_Ofinite(tc_sum(X6,X5),c_Sum__Type_OPlus(X6,X5,X4,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
fof(fact_atLeastLessThan__subset__iff,axiom,
! [X44,X26,X14,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X6,X13,X14),c_SetInterval_Oord__class_OatLeastLessThan(X6,X26,X44))
=> ( c_Orderings_Oord__class_Oless__eq(X6,X14,X13)
| ( c_Orderings_Oord__class_Oless__eq(X6,X26,X13)
& c_Orderings_Oord__class_Oless__eq(X6,X14,X44) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X57,X22,X18,X19,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X19,X18),c_Groups_Oplus__class_Oplus(X6,X22,X57)) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),c_Groups_Oplus__class_Oplus(X6,X18,X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_Plus__eq__empty__conv,axiom,
! [X7,X4,X5,X6] :
( c_Sum__Type_OPlus(X6,X5,X4,X7) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X6,X5),tc_HOL_Obool))
<=> ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
& X7 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).
fof(fact_finite__imageI,axiom,
! [X11,X5,X12,X6] :
( c_Finite__Set_Ofinite(X6,X12)
=> c_Finite__Set_Ofinite(X5,c_Set_Oimage(X6,X5,X11,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_inj__eq,axiom,
! [X9,X8,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> ( hAPP(X2,X8) = hAPP(X2,X9)
<=> X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
fof(fact_injD,axiom,
! [X9,X8,X2,X5,X6] :
( c_Fun_Oinj__on(X6,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> ( hAPP(X2,X8) = hAPP(X2,X9)
=> X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
fof(fact_setsum__eq__0__iff,axiom,
! [X2,X12,X6] :
( c_Finite__Set_Ofinite(X6,X12)
=> ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat,X2,X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ! [X3] :
( c_member(X6,X3,X12)
=> 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_add__less__cancel__right,axiom,
! [X14,X26,X13,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X13,X26),c_Groups_Oplus__class_Oplus(X6,X14,X26))
<=> c_Orderings_Oord__class_Oless(X6,X13,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__right,axiom,
! [X18,X22,X19,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),c_Groups_Oplus__class_Oplus(X6,X18,X22))
=> c_Orderings_Oord__class_Oless(X6,X19,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__left,axiom,
! [X14,X13,X26,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X26,X13),c_Groups_Oplus__class_Oplus(X6,X26,X14))
<=> c_Orderings_Oord__class_Oless(X6,X13,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__imp__less__left,axiom,
! [X18,X19,X22,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X22,X19),c_Groups_Oplus__class_Oplus(X6,X22,X18))
=> c_Orderings_Oord__class_Oless(X6,X19,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__le__cancel__right,axiom,
! [X14,X26,X13,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X13,X26),c_Groups_Oplus__class_Oplus(X6,X14,X26))
<=> c_Orderings_Oord__class_Oless__eq(X6,X13,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__right,axiom,
! [X18,X22,X19,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),c_Groups_Oplus__class_Oplus(X6,X18,X22))
=> c_Orderings_Oord__class_Oless__eq(X6,X19,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__left,axiom,
! [X14,X13,X26,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X26,X13),c_Groups_Oplus__class_Oplus(X6,X26,X14))
<=> c_Orderings_Oord__class_Oless__eq(X6,X13,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__le__imp__le__left,axiom,
! [X18,X19,X22,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X22,X19),c_Groups_Oplus__class_Oplus(X6,X22,X18))
=> c_Orderings_Oord__class_Oless__eq(X6,X19,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X29,X34,X45] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X29))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X29,X34,X45] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X29))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_empty__is__image,axiom,
! [X4,X2,X5,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = c_Set_Oimage(X5,X6,X2,X4)
<=> X4 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).
fof(fact_image__is__empty,axiom,
! [X4,X2,X6,X5] :
( c_Set_Oimage(X5,X6,X2,X4) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> X4 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).
fof(fact_finite__fun__UNIVD1,axiom,
! [X5,X6] :
( c_Finite__Set_Ofinite(tc_fun(X6,X5),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X6,X5),tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
fof(fact_add__strict__mono,axiom,
! [X57,X22,X18,X19,X6] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X19,X18)
=> ( c_Orderings_Oord__class_Oless(X6,X22,X57)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),c_Groups_Oplus__class_Oplus(X6,X18,X57)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X57,X22,X18,X19,X6] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X19,X18)
=> ( c_Orderings_Oord__class_Oless(X6,X22,X57)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),c_Groups_Oplus__class_Oplus(X6,X18,X57)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X57,X22,X18,X19,X6] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X19,X18)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X22,X57)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),c_Groups_Oplus__class_Oplus(X6,X18,X57)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__mono,axiom,
! [X57,X22,X18,X19,X6] :
( class_Groups_Oordered__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X19,X18)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X22,X57)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),c_Groups_Oplus__class_Oplus(X6,X18,X57)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_image__Suc__atLeastAtMost,axiom,
! [X51,X47] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X47,X51)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X47),hAPP(c_Nat_OSuc,X51)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).
fof(fact_image__Suc__atLeastLessThan,axiom,
! [X51,X47] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X47,X51)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X47),hAPP(c_Nat_OSuc,X51)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [X5,X6] : c_Sum__Type_OPlus(X6,X5,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X6,X5),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_add__less__mono,axiom,
! [X56,X39,X40,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X40)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,X56)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X39),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X56)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_add__le__mono,axiom,
! [X56,X39,X40,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X40)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X56)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X39),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X56)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_singletonE,axiom,
! [X13,X14,X6] :
( c_member(X6,X14,c_Set_Oinsert(X6,X13,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))))
=> X14 = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
fof(fact_singleton__iff,axiom,
! [X13,X14,X6] :
( c_member(X6,X14,c_Set_Oinsert(X6,X13,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))))
<=> X14 = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
fof(fact_all__nat__less,axiom,
! [X21,X29] :
( ! [X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X29)
=> hBOOL(hAPP(X21,X30)) )
<=> ! [X3] :
( c_member(tc_Nat_Onat,X3,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29))
=> hBOOL(hAPP(X21,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less) ).
fof(fact_all__nat__less__eq,axiom,
! [X21,X29] :
( ! [X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X29)
=> hBOOL(hAPP(X21,X30)) )
<=> ! [X3] :
( c_member(tc_Nat_Onat,X3,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29))
=> hBOOL(hAPP(X21,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
fof(fact_insert__code,axiom,
! [X8,X4,X9,X6] :
( hBOOL(hAPP(c_Set_Oinsert(X6,X9,X4),X8))
<=> ( X9 = X8
| hBOOL(hAPP(X4,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_insert__mono,axiom,
! [X13,X63,X33,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X33,X63)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Set_Oinsert(X6,X13,X33),c_Set_Oinsert(X6,X13,X63)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(fact_finite__Prod__UNIV,axiom,
! [X5,X6] :
( c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> ( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(tc_prod(X6,X5),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X6,X5),tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [X5,X6] :
( c_Finite__Set_Ofinite(tc_sum(X6,X5),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X6,X5),tc_HOL_Obool)))
<=> ( c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
& c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_insert__subset,axiom,
! [X7,X4,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Set_Oinsert(X6,X8,X4),X7)
<=> ( c_member(X6,X8,X7)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(fact_folding__one__idem_Osubset__idem,axiom,
! [X7,X4,X12,X2,X6] :
( c_Finite__Set_Ofolding__one__idem(X6,X2,X12)
=> ( c_Finite__Set_Ofinite(X6,X4)
=> ( X7 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X4)
=> hAPP(hAPP(X2,hAPP(X12,X7)),hAPP(X12,X4)) = hAPP(X12,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
fof(fact_card__psubset,axiom,
! [X4,X7,X6] :
( c_Finite__Set_Ofinite(X6,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X6,X7))
=> c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
fof(fact_ex__nat__less,axiom,
! [X21,X29] :
( ? [X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X29)
& hBOOL(hAPP(X21,X30)) )
<=> ? [X3] :
( c_member(tc_Nat_Onat,X3,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29))
& hBOOL(hAPP(X21,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less) ).
fof(fact_ex__nat__less__eq,axiom,
! [X21,X29] :
( ? [X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X29)
& hBOOL(hAPP(X21,X30)) )
<=> ? [X3] :
( c_member(tc_Nat_Onat,X3,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29))
& hBOOL(hAPP(X21,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
fof(fact_Ints__odd__nonzero,axiom,
! [X13,X6] :
( class_Int_Oring__char__0(X6)
=> ( c_member(X6,X13,c_Int_Oring__1__class_OInts(X6))
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,c_Groups_Oone__class_Oone(X6),X13),X13) != c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).
fof(fact_atLeastAtMostSuc__conv,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29)) = c_Set_Oinsert(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMostSuc__conv) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [X5,X6] :
( c_Finite__Set_Ofinite(tc_fun(X6,X5),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X6,X5),tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_add__neg__neg,axiom,
! [X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X19,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless(X6,X18,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X19,X18),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__nonpos__neg,axiom,
! [X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X19,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless(X6,X18,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X19,X18),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X19,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless__eq(X6,X18,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X19,X18),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X19,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless__eq(X6,X18,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X19,X18),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_Ints__add,axiom,
! [X14,X13,X6] :
( class_Rings_Oring__1(X6)
=> ( c_member(X6,X13,c_Int_Oring__1__class_OInts(X6))
=> ( c_member(X6,X14,c_Int_Oring__1__class_OInts(X6))
=> c_member(X6,c_Groups_Oplus__class_Oplus(X6,X13,X14),c_Int_Oring__1__class_OInts(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__add) ).
fof(fact_add__pos__pos,axiom,
! [X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X19)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X18)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X19,X18)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__nonneg__pos,axiom,
! [X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X19)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X18)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X19,X18)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X19)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X18)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X19,X18)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X19)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X18)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X19,X18)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_add__gr__0,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X29))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_add__strict__right__mono,axiom,
! [X22,X18,X19,X6] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X19,X18)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),c_Groups_Oplus__class_Oplus(X6,X18,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X22,X18,X19,X6] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X19,X18)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X22,X19),c_Groups_Oplus__class_Oplus(X6,X22,X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_add__right__mono,axiom,
! [X22,X18,X19,X6] :
( class_Groups_Oordered__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X19,X18)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),c_Groups_Oplus__class_Oplus(X6,X18,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X22,X18,X19,X6] :
( class_Groups_Oordered__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X19,X18)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X22,X19),c_Groups_Oplus__class_Oplus(X6,X22,X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_atLeastLessThan__eq__iff,axiom,
! [X44,X26,X14,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X13,X14)
=> ( c_Orderings_Oord__class_Oless(X6,X26,X44)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X6,X13,X14) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X26,X44)
<=> ( X13 = X26
& X14 = X44 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
fof(fact_atLeastLessThan__inj_I1_J,axiom,
! [X44,X26,X14,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X6,X13,X14) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X26,X44)
=> ( c_Orderings_Oord__class_Oless(X6,X13,X14)
=> ( c_Orderings_Oord__class_Oless(X6,X26,X44)
=> X13 = X26 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
fof(fact_atLeastLessThan__inj_I2_J,axiom,
! [X44,X26,X14,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X6,X13,X14) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X26,X44)
=> ( c_Orderings_Oord__class_Oless(X6,X13,X14)
=> ( c_Orderings_Oord__class_Oless(X6,X26,X44)
=> X14 = X44 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
fof(fact_pos__add__strict,axiom,
! [X22,X18,X19,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X19)
=> ( c_Orderings_Oord__class_Oless(X6,X18,X22)
=> c_Orderings_Oord__class_Oless(X6,X18,c_Groups_Oplus__class_Oplus(X6,X19,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__strict__increasing2,axiom,
! [X22,X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X19)
=> ( c_Orderings_Oord__class_Oless(X6,X18,X22)
=> c_Orderings_Oord__class_Oless(X6,X18,c_Groups_Oplus__class_Oplus(X6,X19,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X22,X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X19)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X18,X22)
=> c_Orderings_Oord__class_Oless(X6,X18,c_Groups_Oplus__class_Oplus(X6,X19,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__increasing,axiom,
! [X22,X18,X19,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X19)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X18,X22)
=> c_Orderings_Oord__class_Oless__eq(X6,X18,c_Groups_Oplus__class_Oplus(X6,X19,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X19,X18,X22,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X22)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X18,X19)
=> c_Orderings_Oord__class_Oless__eq(X6,X18,c_Groups_Oplus__class_Oplus(X6,X19,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__less__mono1,axiom,
! [X39,X40,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X40)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X39),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_add__le__mono1,axiom,
! [X39,X40,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X40)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X39),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_card__insert__le,axiom,
! [X8,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X6,c_Set_Oinsert(X6,X8,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).
fof(fact_singleton__inject,axiom,
! [X14,X13,X6] :
( c_Set_Oinsert(X6,X13,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = c_Set_Oinsert(X6,X14,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))
=> X13 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
fof(fact_ord_OlessThan__iff,axiom,
! [X45,X48,X47,X6] :
( c_member(X6,X47,c_SetInterval_Oord_OlessThan(X6,X48,X45))
<=> hBOOL(hAPP(hAPP(X48,X47),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
fof(fact_ord_OatMost__iff,axiom,
! [X45,X46,X47,X6] :
( c_member(X6,X47,c_SetInterval_Oord_OatMost(X6,X46,X45))
<=> hBOOL(hAPP(hAPP(X46,X47),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
fof(fact_ord_OgreaterThan__iff,axiom,
! [X45,X48,X47,X6] :
( c_member(X6,X47,c_SetInterval_Oord_OgreaterThan(X6,X48,X45))
<=> hBOOL(hAPP(hAPP(X48,X45),X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
fof(fact_ord_OatLeast__iff,axiom,
! [X45,X46,X47,X6] :
( c_member(X6,X47,c_SetInterval_Oord_OatLeast(X6,X46,X45))
<=> hBOOL(hAPP(hAPP(X46,X45),X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X13,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X13,X13))
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X13,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X13,X13))
<=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_even__less__0__iff,axiom,
! [X13,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X13,X13),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless(X6,X13,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X13,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X13,X13),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless(X6,X13,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X13,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X13,X13),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless__eq(X6,X13,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X22,X18,X19,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X19,X18),X22) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X22,X18,X19,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X19,X18),X22) = c_Groups_Oplus__class_Oplus(X6,X19,c_Groups_Oplus__class_Oplus(X6,X18,X22)) ),
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,
! [X22,X18,X19,X6] :
( class_Groups_Oab__semigroup__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X19,X18),X22) = c_Groups_Oplus__class_Oplus(X6,X19,c_Groups_Oplus__class_Oplus(X6,X18,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X57,X22,X19,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X19,c_Groups_Oplus__class_Oplus(X6,X22,X57)) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X19,X22),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X57,X22,X19,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X19,c_Groups_Oplus__class_Oplus(X6,X22,X57)) = c_Groups_Oplus__class_Oplus(X6,X22,c_Groups_Oplus__class_Oplus(X6,X19,X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_image__empty,axiom,
! [X2,X6,X5] : c_Set_Oimage(X5,X6,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
fof(fact_folding__one__idem_Oinsert__idem,axiom,
! [X8,X4,X12,X2,X6] :
( c_Finite__Set_Ofolding__one__idem(X6,X2,X12)
=> ( c_Finite__Set_Ofinite(X6,X4)
=> ( X4 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> hAPP(X12,c_Set_Oinsert(X6,X8,X4)) = hAPP(hAPP(X2,X8),hAPP(X12,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).
fof(fact_insert__commute,axiom,
! [X4,X9,X8,X6] : c_Set_Oinsert(X6,X8,c_Set_Oinsert(X6,X9,X4)) = c_Set_Oinsert(X6,X9,c_Set_Oinsert(X6,X8,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(fact_psubset__trans,axiom,
! [X33,X7,X4,X6] :
( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X7,X33)
=> c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(fact_subset__psubset__trans,axiom,
! [X33,X7,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X7,X33)
=> c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X33,X7,X4,X6] :
( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X33)
=> c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_subset__trans,axiom,
! [X33,X7,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_nat__add__assoc,axiom,
! [X39,X25,X35] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X25),X39) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X39)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_nat__add__left__commute,axiom,
! [X23,X17,X16] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X23)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X23)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_card__seteq,axiom,
! [X4,X7,X6] :
( c_Finite__Set_Ofinite(X6,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X7),c_Finite__Set_Ocard(X6,X4))
=> X4 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
fof(fact_insert__iff,axiom,
! [X4,X14,X13,X6] :
( c_member(X6,X13,c_Set_Oinsert(X6,X14,X4))
<=> ( X13 = X14
| c_member(X6,X13,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
fof(fact_insertE,axiom,
! [X4,X14,X13,X6] :
( c_member(X6,X13,c_Set_Oinsert(X6,X14,X4))
=> ( X13 != X14
=> c_member(X6,X13,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_setsum_Oempty,axiom,
! [X1,X5,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6,X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oempty) ).
fof(fact_setsum__empty,axiom,
! [X2,X5,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__empty) ).
fof(fact_subset__insertI2,axiom,
! [X14,X7,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oinsert(X6,X14,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(fact_less__add__eq__less,axiom,
! [X25,X35,X56,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,X56)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X56) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X25)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_add__lessD1,axiom,
! [X39,X40,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X40),X39)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__leD1,axiom,
! [X25,X39,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X39),X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X25,X39,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X39),X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_inj__on__empty,axiom,
! [X2,X5,X6] : c_Fun_Oinj__on(X6,X5,X2,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X9,X8,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X8)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X9)
=> ( c_Groups_Oplus__class_Oplus(X6,X8,X9) = c_Groups_Ozero__class_Ozero(X6)
<=> ( X8 = c_Groups_Ozero__class_Ozero(X6)
& X9 = c_Groups_Ozero__class_Ozero(X6) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_finite__UNIV__card__ge__0,axiom,
! [X6] :
( c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(fact_less__add__Suc1,axiom,
! [X35,X41] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X35))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X35,X41] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X41))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_folding__one__idem_Oin__idem,axiom,
! [X8,X4,X12,X2,X6] :
( c_Finite__Set_Ofolding__one__idem(X6,X2,X12)
=> ( c_Finite__Set_Ofinite(X6,X4)
=> ( c_member(X6,X8,X4)
=> hAPP(hAPP(X2,X8),hAPP(X12,X4)) = hAPP(X12,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
fof(fact_greaterThan__subset__iff,axiom,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X6,X8),c_SetInterval_Oord__class_OgreaterThan(X6,X9))
<=> c_Orderings_Oord__class_Oless__eq(X6,X9,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).
fof(fact_set__rev__mp,axiom,
! [X7,X4,X8,X6] :
( c_member(X6,X8,X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_member(X6,X8,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_psubsetD,axiom,
! [X26,X7,X4,X6] :
( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_member(X6,X26,X4)
=> c_member(X6,X26,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(fact_set__mp,axiom,
! [X8,X7,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_member(X6,X8,X4)
=> c_member(X6,X8,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_in__mono,axiom,
! [X8,X7,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_member(X6,X8,X4)
=> c_member(X6,X8,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_subsetD,axiom,
! [X26,X7,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_member(X6,X26,X4)
=> c_member(X6,X26,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_atLeastAtMost__singleton__iff,axiom,
! [X26,X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14) = c_Set_Oinsert(X6,X26,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))
<=> ( X13 = X14
& X14 = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [X4,X6] :
( c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X6,X4) = c_Finite__Set_Ocard(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> X4 = c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_less__iff__Suc__add,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29)
<=> ? [X55] : X29 = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_psubset__card__mono,axiom,
! [X4,X7,X6] :
( c_Finite__Set_Ofinite(X6,X7)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X6,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_card__mono,axiom,
! [X4,X7,X6] :
( c_Finite__Set_Ofinite(X6,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X6,X4),c_Finite__Set_Ocard(X6,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
fof(fact_insertI2,axiom,
! [X14,X7,X13,X6] :
( c_member(X6,X13,X7)
=> c_member(X6,X13,c_Set_Oinsert(X6,X14,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
fof(fact_set__eq__subset,axiom,
! [X6,X7,X4] :
( X4 = X7
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X7,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X4)
=> X4 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_less__trans__Suc,axiom,
! [X39,X40,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X40)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X39)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X41),X39) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_inj__Suc,axiom,
! [X38] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(fact_le__funE,axiom,
! [X8,X1,X2,X6,X5] :
( class_Orderings_Oord(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X5),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(X2,X8),hAPP(X1,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_le__funD,axiom,
! [X8,X1,X2,X6,X5] :
( class_Orderings_Oord(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X5),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(X2,X8),hAPP(X1,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_trans__less__add1,axiom,
! [X35,X40,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X40)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X23,X17,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add2,axiom,
! [X35,X40,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X40)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X17,X23,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X23)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__le__add1,axiom,
! [X35,X40,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X40)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X23,X17,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X17)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add2,axiom,
! [X35,X40,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X40)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X17,X23,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_order__less__trans,axiom,
! [X23,X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> ( c_Orderings_Oord__class_Oless(X6,X17,X23)
=> c_Orderings_Oord__class_Oless(X6,X16,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X23,X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X17)
=> ( c_Orderings_Oord__class_Oless(X6,X17,X23)
=> c_Orderings_Oord__class_Oless(X6,X16,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X23,X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X17,X23)
=> c_Orderings_Oord__class_Oless(X6,X16,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X23,X16,X17,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X17,X16)
=> ( c_Orderings_Oord__class_Oless(X6,X23,X17)
=> c_Orderings_Oord__class_Oless(X6,X23,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_xt1_I8_J,axiom,
! [X23,X16,X17,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X17,X16)
=> ( c_Orderings_Oord__class_Oless(X6,X23,X17)
=> c_Orderings_Oord__class_Oless(X6,X23,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X23,X16,X17,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X17,X16)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,X17)
=> c_Orderings_Oord__class_Oless(X6,X23,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__trans,axiom,
! [X23,X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X17,X23)
=> c_Orderings_Oord__class_Oless__eq(X6,X16,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X23,X16,X17,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X17,X16)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,X17)
=> c_Orderings_Oord__class_Oless__eq(X6,X23,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_subset__empty,axiom,
! [X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))
<=> X4 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
fof(fact_the__elem__eq,axiom,
! [X8,X6] : c_Set_Othe__elem(X6,c_Set_Oinsert(X6,X8,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__eq) ).
fof(fact_le__trans,axiom,
! [X39,X40,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X40)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X39) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_finite__option__UNIV,axiom,
! [X6] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X6),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X6),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_insert__absorb2,axiom,
! [X4,X8,X6] : c_Set_Oinsert(X6,X8,c_Set_Oinsert(X6,X8,X4)) = c_Set_Oinsert(X6,X8,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
fof(fact_Suc__less__SucD,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35),hAPP(c_Nat_OSuc,X25))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__less__eq,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34),hAPP(c_Nat_OSuc,X29))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__le__mono,axiom,
! [X34,X29] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),hAPP(c_Nat_OSuc,X34))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_le__less__Suc__eq,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,hAPP(c_Nat_OSuc,X34))
<=> X29 = X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_finite__insert,axiom,
! [X4,X13,X6] :
( c_Finite__Set_Ofinite(X6,c_Set_Oinsert(X6,X13,X4))
<=> c_Finite__Set_Ofinite(X6,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))
<=> ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X54] :
( X34 = hAPP(c_Nat_OSuc,X54)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X54,X29) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [X7,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
<=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X7)
| X4 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__eq,axiom,
! [X7,X4,X6] :
( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X7)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
& X4 != X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(fact_Ints__double__eq__0__iff,axiom,
! [X13,X6] :
( class_Int_Oring__char__0(X6)
=> ( c_member(X6,X13,c_Int_Oring__1__class_OInts(X6))
=> ( c_Groups_Oplus__class_Oplus(X6,X13,X13) = c_Groups_Ozero__class_Ozero(X6)
<=> X13 = c_Groups_Ozero__class_Ozero(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_predicate1D,axiom,
! [X8,X20,X21,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X21,X20)
=> ( hBOOL(hAPP(X21,X8))
=> hBOOL(hAPP(X20,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X20,X6,X8,X21] :
( hBOOL(hAPP(X21,X8))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X21,X20)
=> hBOOL(hAPP(X20,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_psubset__imp__subset,axiom,
! [X7,X4,X6] :
( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_zero__less__two,axiom,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Oone__class_Oone(X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_add__Suc,axiom,
! [X25,X35] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35),X25) = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__right,axiom,
! [X25,X35] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X25)) = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_nat__less__cases,axiom,
! [X21,X29,X34] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29)
=> hBOOL(hAPP(hAPP(X21,X29),X34)) )
=> ( ( X34 = X29
=> hBOOL(hAPP(hAPP(X21,X29),X34)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X34)
=> hBOOL(hAPP(hAPP(X21,X29),X34)) )
=> hBOOL(hAPP(hAPP(X21,X29),X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_greaterThan__iff,axiom,
! [X45,X47,X6] :
( class_Orderings_Oord(X6)
=> ( c_member(X6,X47,c_SetInterval_Oord__class_OgreaterThan(X6,X45))
<=> c_Orderings_Oord__class_Oless(X6,X45,X47) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__iff) ).
fof(fact_le__Suc__eq,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
| X34 = hAPP(c_Nat_OSuc,X29) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_subset__insertI,axiom,
! [X13,X7,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,c_Set_Oinsert(X6,X13,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(fact_Suc__mono,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35),hAPP(c_Nat_OSuc,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_xt1_I5_J,axiom,
! [X16,X17,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X17,X16)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X17)
=> X16 = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__antisym,axiom,
! [X17,X16,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X17,X16)
=> X16 = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_order__antisym__conv,axiom,
! [X8,X9,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X9,X8)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
<=> X8 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__iff,axiom,
! [X9,X8,X6] :
( class_Orderings_Oorder(X6)
=> ( X8 = X9
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
& c_Orderings_Oord__class_Oless__eq(X6,X9,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_less__add__one,axiom,
! [X19,X6] :
( class_Rings_Olinordered__semidom(X6)
=> c_Orderings_Oord__class_Oless(X6,X19,c_Groups_Oplus__class_Oplus(X6,X19,c_Groups_Oone__class_Oone(X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_add__right__imp__eq,axiom,
! [X22,X19,X18,X6] :
( class_Groups_Ocancel__semigroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X18,X19) = c_Groups_Oplus__class_Oplus(X6,X22,X19)
=> X18 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X26,X13,X14,X6] :
( class_Groups_Ocancel__semigroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X14,X13) = c_Groups_Oplus__class_Oplus(X6,X26,X13)
<=> X14 = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X22,X18,X19,X6] :
( class_Groups_Ocancel__ab__semigroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X19,X18) = c_Groups_Oplus__class_Oplus(X6,X19,X22)
=> X18 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X22,X18,X19,X6] :
( class_Groups_Ocancel__semigroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X19,X18) = c_Groups_Oplus__class_Oplus(X6,X19,X22)
=> X18 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X26,X14,X13,X6] :
( class_Groups_Ocancel__semigroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X13,X14) = c_Groups_Oplus__class_Oplus(X6,X13,X26)
<=> X14 = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_less__Suc__eq,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29)
| X34 = X29 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_atLeastatMost__empty,axiom,
! [X13,X14,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X14,X13)
=> c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty) ).
fof(fact_atLeastLessThan__empty,axiom,
! [X13,X14,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X14,X13)
=> c_SetInterval_Oord__class_OatLeastLessThan(X6,X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).
fof(fact_atLeastLessThan__singleton,axiom,
! [X34] : c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X34)) = c_Set_Oinsert(tc_Nat_Onat,X34,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_Suc__lessI,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25)
=> ( hAPP(c_Nat_OSuc,X35) != X25
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_card__gt__0__iff,axiom,
! [X4,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X6,X4))
<=> ( X4 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
& c_Finite__Set_Ofinite(X6,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
fof(fact_Suc__lessD,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35),X25)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_less__eq__Suc__le,axiom,
! [X34,X29] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X34)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__le__eq,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34),X29)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_Suc__le__lessD,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35),X25)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_Suc__leD,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35),X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_less__Suc__eq__le,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_atLeastAtMost__singleton_H,axiom,
! [X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( X13 = X14
=> c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14) = c_Set_Oinsert(X6,X13,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton_H) ).
fof(fact_le__antisym,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X35)
=> X35 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_nat__add__right__cancel,axiom,
! [X29,X45,X34] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X45) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X45)
<=> X34 = X29 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X29,X34,X45] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X34) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X29)
<=> X34 = X29 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_atLeastAtMost__singleton,axiom,
! [X13,X6] :
( class_Orderings_Oorder(X6)
=> c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X13) = c_Set_Oinsert(X6,X13,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton) ).
fof(fact_le__iff__add,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
<=> ? [X55] : X29 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X38] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X38)
<=> ? [X30] :
! [X3] :
( c_member(tc_Nat_Onat,X3,X38)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X30) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X38] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X38)
<=> ? [X30] :
! [X3] :
( c_member(tc_Nat_Onat,X3,X38)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X30) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_insertI1,axiom,
! [X7,X13,X6] : c_member(X6,X13,c_Set_Oinsert(X6,X13,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_Suc__leI,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_less__SucI,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_le__imp__less__Suc,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_le__SucI,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_finite__subset,axiom,
! [X7,X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ( c_Finite__Set_Ofinite(X6,X7)
=> c_Finite__Set_Ofinite(X6,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(fact_rev__finite__subset,axiom,
! [X4,X7,X6] :
( c_Finite__Set_Ofinite(X6,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> c_Finite__Set_Ofinite(X6,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_le__add1,axiom,
! [X35,X25] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X35)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X35,X25] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_add__Suc__shift,axiom,
! [X25,X35] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35),X25) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_xt1_I11_J,axiom,
! [X19,X18,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X18,X19)
=> ( X19 != X18
=> c_Orderings_Oord__class_Oless(X6,X18,X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X18,X19,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X19,X18)
=> ( X19 != X18
=> c_Orderings_Oord__class_Oless(X6,X19,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X17,X16,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X17)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
| X16 = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X18,X19,X6] :
( class_Orderings_Oorder(X6)
=> ( X19 != X18
=> ( c_Orderings_Oord__class_Oless__eq(X6,X19,X18)
=> c_Orderings_Oord__class_Oless(X6,X19,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__less,axiom,
! [X9,X8,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
<=> ( c_Orderings_Oord__class_Oless(X6,X8,X9)
| X8 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__le,axiom,
! [X9,X8,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
& X8 != X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_xt1_I12_J,axiom,
! [X18,X19,X6] :
( class_Orderings_Oorder(X6)
=> ( X19 != X18
=> ( c_Orderings_Oord__class_Oless__eq(X6,X18,X19)
=> c_Orderings_Oord__class_Oless(X6,X18,X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_order__less__imp__le,axiom,
! [X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> c_Orderings_Oord__class_Oless__eq(X6,X16,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_finite_OinsertI,axiom,
! [X13,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> c_Finite__Set_Ofinite(X6,c_Set_Oinsert(X6,X13,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_card__ge__0__finite,axiom,
! [X4,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X6,X4))
=> c_Finite__Set_Ofinite(X6,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
fof(fact_insert__absorb,axiom,
! [X4,X13,X6] :
( c_member(X6,X13,X4)
=> c_Set_Oinsert(X6,X13,X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_one__is__add,axiom,
! [X29,X34] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X29)
<=> ( ( X34 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X29 = 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_add__is__1,axiom,
! [X29,X34] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X29) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X34 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X29 = 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_nat_Osize_I4_J,axiom,
! [X58] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X58)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,X58),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_le__neq__implies__less,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25)
=> ( X35 != X25
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29)
| X34 = X29 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__less__le,axiom,
! [X29,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
& X34 != X29 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X17,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X17)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X25,X35] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25)
| X35 = X25 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_less__imp__le__nat,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_top1I,axiom,
! [X8,X6] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_less__Suc0,axiom,
! [X29] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_ex__in__conv,axiom,
! [X4,X6] :
( ? [X3] : c_member(X6,X3,X4)
<=> X4 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
fof(fact_empty__subsetI,axiom,
! [X4,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
fof(fact_subset__UNIV,axiom,
! [X4,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
! [X31,X32] : c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X32,hAPP(c_Nat_OSuc,X31)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X32,X31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).
fof(fact_empty__not__insert,axiom,
! [X4,X13,X6] : c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) != c_Set_Oinsert(X6,X13,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
fof(fact_insert__not__empty,axiom,
! [X4,X13,X6] : c_Set_Oinsert(X6,X13,X4) != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
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_folding__one__idem_Oidem,axiom,
! [X8,X12,X2,X6] :
( c_Finite__Set_Ofolding__one__idem(X6,X2,X12)
=> hAPP(hAPP(X2,X8),X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
fof(fact_card_Oneutral,axiom,
! [X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( ( ? [X3] : c_member(X6,X3,X4)
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> c_Finite__Set_Ocard(X6,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oneutral) ).
fof(fact_linorder__neq__iff,axiom,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( X8 != X9
<=> ( c_Orderings_Oord__class_Oless(X6,X8,X9)
| c_Orderings_Oord__class_Oless(X6,X9,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
| X16 = X17
| c_Orderings_Oord__class_Oless(X6,X17,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_linorder__le__less__linear,axiom,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X17)
| c_Orderings_Oord__class_Oless(X6,X17,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_linorder__linear,axiom,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X17)
| c_Orderings_Oord__class_Oless__eq(X6,X17,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_mem__def,axiom,
! [X4,X8,X6] :
( c_member(X6,X8,X4)
<=> hBOOL(hAPP(X4,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_finite__atLeastAtMost,axiom,
! [X31,X32] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X32,X31)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
fof(fact_finite__atLeastLessThan,axiom,
! [X31,X32] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X32,X31)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X22,X19,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X19,X22) = c_Groups_Oplus__class_Oplus(X6,X22,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_nat_Osize_I2_J,axiom,
! [X58] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X58)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(X58),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_nat__neq__iff,axiom,
! [X29,X34] :
( X34 != X29
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X34) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_gr0__conv__Suc,axiom,
! [X29] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29)
<=> ? [X30] : X29 = hAPP(c_Nat_OSuc,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_nat__le__linear,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_iso__tuple__UNIV__I,axiom,
! [X8,X6] : c_member(X6,X8,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(fact_UNIV__I,axiom,
! [X8,X6] : c_member(X6,X8,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_nat__add__commute,axiom,
! [X25,X35] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X25) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_double__eq__0__iff,axiom,
! [X13,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X13,X13) = c_Groups_Ozero__class_Ozero(X6)
<=> X13 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X13,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Groups_Ozero__class_Ozero(X6) = c_Groups_Oplus__class_Oplus(X6,X13,X13)
<=> X13 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0__iff,axiom,
! [X13,X14,X6] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6)
=> ( X14 = c_Groups_Oplus__class_Oplus(X6,X14,X13)
<=> X13 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_eq__mem,axiom,
! [X9,X8,X6] :
( c_member(X6,X8,c_fequal(X9))
<=> X8 = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X17,X16,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> X17 != X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X17,X16,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> X16 != X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X17,X16,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> X16 != X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_neq0__conv,axiom,
! [X29] :
( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_le__0__eq,axiom,
! [X29] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_infinite__UNIV__nat,axiom,
~ 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_add__is__0,axiom,
! [X29,X34] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X29) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_gr__implies__not0,axiom,
! [X25,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25)
=> X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_add__eq__self__zero,axiom,
! [X25,X35] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X25) = X35
=> X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_less__not__refl3,axiom,
! [X36,X37] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X36)
=> X37 != X36 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X35,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X35)
=> X35 != X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_UNIV__not__empty,axiom,
! [X6] : c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
fof(fact_bot__apply,axiom,
! [X8,X5,X6] :
( class_Orderings_Obot(X6)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,X6)),X8) = c_Orderings_Obot__class_Obot(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(fact_top__apply,axiom,
! [X8,X5,X6] :
( class_Orderings_Otop(X6)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,X6)),X8) = c_Orderings_Otop__class_Otop(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_equalityD1,axiom,
! [X6,X7,X4] :
( X4 = X7
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X6,X7,X4] :
( X4 = X7
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_atLeastLessThan0,axiom,
! [X34] : c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,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_zero__less__Suc,axiom,
! [X25] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_subset__refl,axiom,
! [X4,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_lessI,axiom,
! [X25] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,hAPP(c_Nat_OSuc,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_zero__less__one,axiom,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oone__class_Oone(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_zero__le__one,axiom,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oone__class_Oone(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_Ints__1,axiom,
! [X6] :
( class_Rings_Oring__1(X6)
=> c_member(X6,c_Groups_Oone__class_Oone(X6),c_Int_Oring__1__class_OInts(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__1) ).
fof(fact_Ints__0,axiom,
! [X6] :
( class_Rings_Oring__1(X6)
=> c_member(X6,c_Groups_Ozero__class_Ozero(X6),c_Int_Oring__1__class_OInts(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__0) ).
fof(fact_finite__UNIV,axiom,
! [X6] :
( class_Finite__Set_Ofinite(X6)
=> c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X19,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ozero__class_Ozero(X6),X19) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0__left,axiom,
! [X19,X6] :
( class_Groups_Omonoid__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ozero__class_Ozero(X6),X19) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [X19,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ozero__class_Ozero(X6),X19) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X19,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X19,c_Groups_Ozero__class_Ozero(X6)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add__0__right,axiom,
! [X19,X6] :
( class_Groups_Omonoid__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,X19,c_Groups_Ozero__class_Ozero(X6)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X19,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,X19,c_Groups_Ozero__class_Ozero(X6)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_card_Oempty,axiom,
! [X6] : c_Finite__Set_Ocard(X6,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oempty) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X25] : hAPP(c_Nat_OSuc,X25) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_Suc__eq__plus1,axiom,
! [X25] : hAPP(c_Nat_OSuc,X25) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_bot__least,axiom,
! [X16,X6] :
( class_Orderings_Obot(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Orderings_Obot__class_Obot(X6),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
fof(fact_top__greatest,axiom,
! [X16,X6] :
( class_Orderings_Otop(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X16,c_Orderings_Otop__class_Otop(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(fact_finite_Oequations_I1_J,axiom,
! [X6] : c_Finite__Set_Ofinite(X6,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
fof(fact_finite_OemptyI,axiom,
! [X6] : c_Finite__Set_Ofinite(X6,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
fof(fact_order__eq__refl,axiom,
! [X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( X16 = X17
=> c_Orderings_Oord__class_Oless__eq(X6,X16,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_order__refl,axiom,
! [X16,X6] :
( class_Orderings_Opreorder(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X16,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_gr0I,axiom,
! [X25] :
( X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X25] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X35] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X35,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_eq__imp__le,axiom,
! [X25,X35] :
( X35 = X25
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X25] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X25] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_greaterThan__eq__iff,axiom,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_SetInterval_Oord__class_OgreaterThan(X6,X8) = c_SetInterval_Oord__class_OgreaterThan(X6,X9)
<=> X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).
fof(fact_le__refl,axiom,
! [X25] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(help_c__fequal__2,axiom,
! [X9,X8] :
( X8 != X9
| hBOOL(hAPP(c_fequal(X8),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [X67,X66] :
( ( class_Finite__Set_Ofinite(X66)
& class_Finite__Set_Ofinite(X67) )
=> class_Finite__Set_Ofinite(tc_prod(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(arity_sum__Finite__Set_Ofinite,axiom,
! [X67,X66] :
( ( class_Finite__Set_Ofinite(X66)
& class_Finite__Set_Ofinite(X67) )
=> class_Finite__Set_Ofinite(tc_sum(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(arity_fun__Finite__Set_Ofinite,axiom,
! [X67,X66] :
( ( class_Finite__Set_Ofinite(X66)
& class_Finite__Set_Ofinite(X67) )
=> class_Finite__Set_Ofinite(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(fact_Suc__inject,axiom,
! [X17,X16] :
( hAPP(c_Nat_OSuc,X16) = hAPP(c_Nat_OSuc,X17)
=> X16 = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(fact_nat_Oinject,axiom,
! [X49,X50] :
( hAPP(c_Nat_OSuc,X50) = hAPP(c_Nat_OSuc,X49)
<=> X50 = X49 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X66,X67] :
( class_Orderings_Oorder(X67)
=> class_Orderings_Oorder(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X66,X67] :
( class_Orderings_Oord(X67)
=> class_Orderings_Oord(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Obot,axiom,
! [X66,X67] :
( class_Orderings_Obot(X67)
=> class_Orderings_Obot(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X66,X67] :
( class_Orderings_Opreorder(X67)
=> class_Orderings_Opreorder(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Orderings_Otop,axiom,
! [X66,X67] :
( class_Orderings_Otop(X67)
=> class_Orderings_Otop(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(fact_Suc__not__Zero,axiom,
! [X35] : hAPP(c_Nat_OSuc,X35) != 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,
! [X52] : hAPP(c_Nat_OSuc,X52) != 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,
! [X35] : hAPP(c_Nat_OSuc,X35) != 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,
! [X35] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X53] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__neq__Suc,axiom,
! [X35] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_finite__code,axiom,
! [X4,X6] :
( class_Finite__Set_Ofinite(X6)
=> c_Finite__Set_Ofinite(X6,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
fof(fact_finite,axiom,
! [X4,X6] :
( class_Finite__Set_Ofinite(X6)
=> c_Finite__Set_Ofinite(X6,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_Suc__n__not__n,axiom,
! [X25] : hAPP(c_Nat_OSuc,X25) != X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X25] : X25 != hAPP(c_Nat_OSuc,X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_zero__neq__one,axiom,
! [X6] :
( class_Rings_Ozero__neq__one(X6)
=> c_Groups_Ozero__class_Ozero(X6) != c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X6] :
( class_Rings_Ozero__neq__one(X6)
=> c_Groups_Oone__class_Oone(X6) != c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
! [X67] :
( class_Finite__Set_Ofinite(X67)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(fact_nat__size,axiom,
! [X25] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X25) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
fof(help_c__fFalse__1,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(conj_1,conjecture,
v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_greaterThan__0,axiom,
c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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_card__UNIV__unit,axiom,
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_finite__indi,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
fof(fact_nat_Osize_I3_J,axiom,
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_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_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_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_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(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
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_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_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
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_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_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
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_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_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(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
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_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_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
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(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
fof(fact_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
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(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(help_c__fTrue__1,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
fof(i_0_519,plain,
! [X4,X2,X5,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(X6,c_Set_Oimage(X5,X6,X2,X4)),c_Finite__Set_Ocard(X5,X4))
=> ~ c_Fun_Oinj__on(X5,X6,X2,X4) ),
inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).
fof(i_0_520,plain,
! [X2,X34,X29,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),X34)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))) = c_Groups_Ozero__class_Ozero(X6) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),X34)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))) = c_Groups_Oplus__class_Oplus(X6,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X29)),hAPP(X2,hAPP(c_Nat_OSuc,X29))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).
fof(i_0_521,plain,
! [X2,X34,X29,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X34)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))) = c_Groups_Ozero__class_Ozero(X6) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X34)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29))) = c_Groups_Oplus__class_Oplus(X6,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,X29)),hAPP(X2,X29)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc]) ).
fof(i_0_522,plain,
! [X2,X13,X12,X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( c_Finite__Set_Ofinite(X6,X12)
=> ( ~ c_member(X6,X13,X12)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X2,c_Set_Oinsert(X6,X13,X12)) = c_Groups_Oplus__class_Oplus(X5,hAPP(X2,X13),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X2,X12)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__insert]) ).
fof(i_0_523,plain,
! [X1,X8,X4,X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( c_Finite__Set_Ofinite(X6,X4)
=> ( ~ c_member(X6,X8,X4)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X1,c_Set_Oinsert(X6,X8,X4)) = c_Groups_Oplus__class_Oplus(X5,hAPP(X1,X8),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X1,X4)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum_Oinsert]) ).
fof(i_0_524,plain,
! [X44,X26,X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14),c_SetInterval_Oord__class_OatLeastAtMost(X6,X26,X44))
<=> ( ( ~ c_Orderings_Oord__class_Oless__eq(X6,X13,X14)
| ( c_Orderings_Oord__class_Oless__eq(X6,X26,X13)
& c_Orderings_Oord__class_Oless__eq(X6,X14,X44)
& ( c_Orderings_Oord__class_Oless(X6,X26,X13)
| c_Orderings_Oord__class_Oless(X6,X14,X44) ) ) )
& c_Orderings_Oord__class_Oless__eq(X6,X26,X44) ) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).
fof(i_0_525,plain,
! [X44,X26,X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14),c_SetInterval_Oord__class_OatLeastAtMost(X6,X26,X44))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X13,X14)
| ( c_Orderings_Oord__class_Oless__eq(X6,X26,X13)
& c_Orderings_Oord__class_Oless__eq(X6,X14,X44) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__subset__iff]) ).
fof(i_0_526,plain,
! [X45,X4,X6] :
( c_Finite__Set_Ocard(X6,X4) = hAPP(c_Nat_OSuc,X45)
<=> ? [X64,X65] :
( X4 = c_Set_Oinsert(X6,X64,X65)
& ~ c_member(X6,X64,X65)
& c_Finite__Set_Ocard(X6,X65) = X45
& ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X65 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__Suc__eq]) ).
fof(i_0_527,plain,
! [X29,X21] :
( ~ hBOOL(hAPP(X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X21,X29))
=> ? [X55] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X29)
& ! [X62] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62,X55)
=> ~ hBOOL(hAPP(X21,X62)) )
& hBOOL(hAPP(X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).
fof(i_0_528,plain,
! [X7,X4,X8,X6] :
( ~ c_member(X6,X8,X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,c_Set_Oinsert(X6,X8,X7))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).
fof(i_0_529,plain,
! [X8,X4,X12,X2,X6] :
( c_Finite__Set_Ofolding__one(X6,X2,X12)
=> ( c_Finite__Set_Ofinite(X6,X4)
=> ( ~ c_member(X6,X8,X4)
=> ( X4 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> hAPP(X12,c_Set_Oinsert(X6,X8,X4)) = hAPP(hAPP(X2,X8),hAPP(X12,X4)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert]) ).
fof(i_0_530,plain,
! [X29,X34] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
=> c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29)) = c_Set_Oinsert(tc_Nat_Onat,X29,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,X29)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
=> c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X29)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastLessThanSuc]) ).
fof(i_0_531,plain,
! [X25,X39,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X39),X25)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X25) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_532,plain,
! [X1,X2,X6,X5] :
( class_Orderings_Oord(X5)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,X5),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X5),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X5),X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_533,plain,
! [X7,X4,X8,X6] :
( ~ c_member(X6,X8,X4)
=> ( ~ c_member(X6,X8,X7)
=> ( c_Set_Oinsert(X6,X8,X4) = c_Set_Oinsert(X6,X8,X7)
<=> X4 = X7 ) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).
fof(i_0_534,plain,
! [X8,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( ~ c_member(X6,X8,X4)
=> c_Finite__Set_Ocard(X6,c_Set_Oinsert(X6,X8,X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(X6,X4)) ) ),
inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).
fof(i_0_535,plain,
! [X2,X4,X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( ~ c_Finite__Set_Ofinite(X6,X4)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X2,X4) = c_Groups_Ozero__class_Ozero(X5) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__infinite]) ).
fof(i_0_536,plain,
! [X1,X4,X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( ~ c_Finite__Set_Ofinite(X6,X4)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X5,X1,X4) = c_Groups_Ozero__class_Ozero(X5) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum_Oinfinite]) ).
fof(i_0_537,plain,
! [X14,X7,X13,X6] :
( ( ~ c_member(X6,X13,X7)
=> X13 = X14 )
=> c_member(X6,X13,c_Set_Oinsert(X6,X14,X7)) ),
inference(fof_simplification,[status(thm)],[fact_insertCI]) ).
fof(i_0_538,plain,
! [X40,X41] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X40),X41),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_539,plain,
! [X41,X40] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X41),X41),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_540,plain,
! [X8,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( ( c_member(X6,X8,X4)
=> c_Finite__Set_Ocard(X6,c_Set_Oinsert(X6,X8,X4)) = c_Finite__Set_Ocard(X6,X4) )
& ( ~ c_member(X6,X8,X4)
=> c_Finite__Set_Ocard(X6,c_Set_Oinsert(X6,X8,X4)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X6,X4)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).
fof(i_0_541,plain,
! [X8,X4,X6] :
( c_Finite__Set_Ofinite(X6,X4)
=> ( ~ c_member(X6,X8,X4)
=> c_Finite__Set_Ocard(X6,c_Set_Oinsert(X6,X8,X4)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X6,X4)) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).
fof(i_0_542,plain,
! [X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14)
<=> ~ c_Orderings_Oord__class_Oless__eq(X6,X13,X14) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).
fof(i_0_543,plain,
! [X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X13,X14)
<=> ~ c_Orderings_Oord__class_Oless(X6,X13,X14) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).
fof(i_0_544,plain,
! [X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X6,X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ~ c_Orderings_Oord__class_Oless__eq(X6,X13,X14) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff]) ).
fof(i_0_545,plain,
! [X14,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X6,X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ~ c_Orderings_Oord__class_Oless(X6,X13,X14) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).
fof(i_0_546,plain,
! [X29,X34] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X29)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X29),X34) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_547,plain,
! [X29,X34] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X29)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,hAPP(c_Nat_OSuc,X34)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_548,plain,
! [X4,X6] : ~ c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
inference(fof_simplification,[status(thm)],[fact_not__psubset__empty]) ).
fof(i_0_549,plain,
! [X9,X8,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X9,X8) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_550,plain,
! [X25,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X25))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X25)
=> X35 = hAPP(c_Nat_OSuc,X25) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_551,plain,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> X8 = X9 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_552,plain,
! [X19,X18,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X18,X19)
=> ~ c_Orderings_Oord__class_Oless(X6,X19,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_553,plain,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> ( c_Orderings_Oord__class_Oless(X6,X9,X8)
| X8 = X9 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_554,plain,
! [X16,X17,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X17,X16)
=> ~ c_Orderings_Oord__class_Oless(X6,X16,X17) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_555,plain,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> c_Orderings_Oord__class_Oless__eq(X6,X9,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_556,plain,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
<=> c_Orderings_Oord__class_Oless(X6,X9,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_557,plain,
! [X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> ~ c_Orderings_Oord__class_Oless(X6,X17,X16) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_558,plain,
! [X18,X19,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X19,X18)
=> ~ c_Orderings_Oord__class_Oless(X6,X18,X19) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_559,plain,
! [X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> ~ c_Orderings_Oord__class_Oless(X6,X17,X16) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_560,plain,
! [X17,X16,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X17)
=> ~ c_Orderings_Oord__class_Oless(X6,X17,X16) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_561,plain,
! [X25,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X25))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X25)
=> X35 = X25 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_562,plain,
! [X35,X25] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X35)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,hAPP(c_Nat_OSuc,X35))
=> X35 = X25 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_563,plain,
! [X34,X29] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X34)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,hAPP(c_Nat_OSuc,X34))
<=> X29 = X34 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_564,plain,
! [X26,X6] : ~ c_member(X6,X26,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
inference(fof_simplification,[status(thm)],[fact_empty__iff]) ).
fof(i_0_565,plain,
! [X13,X6] : ~ c_member(X6,X13,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
inference(fof_simplification,[status(thm)],[fact_emptyE]) ).
fof(i_0_566,plain,
! [X9,X8,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X8,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X9)
<=> X8 = X9 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_567,plain,
! [X13,X6,X4] :
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> ~ c_member(X6,X13,X4) ),
inference(fof_simplification,[status(thm)],[fact_equals0D]) ).
fof(i_0_568,plain,
! [X4,X6] :
( ! [X3] : ~ c_member(X6,X3,X4)
<=> X4 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ),
inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).
fof(i_0_569,plain,
! [X25] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X25),X25),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_570,plain,
! [X17,X16,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( X16 != X17
=> ( ~ c_Orderings_Oord__class_Oless(X6,X16,X17)
=> c_Orderings_Oord__class_Oless(X6,X17,X16) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_571,plain,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X16,X17)
=> ( X16 != X17
=> c_Orderings_Oord__class_Oless(X6,X17,X16) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_572,plain,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( X16 != X17
=> ( ~ c_Orderings_Oord__class_Oless(X6,X16,X17)
=> c_Orderings_Oord__class_Oless(X6,X17,X16) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_573,plain,
! [X8,X9,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X9,X8)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X8,X9)
<=> X8 = X9 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_574,plain,
! [X16,X17,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X17,X16)
=> c_Orderings_Oord__class_Oless(X6,X16,X17) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_575,plain,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X16,X17)
=> c_Orderings_Oord__class_Oless__eq(X6,X17,X16) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_576,plain,
! [X17,X16,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X16,X17)
=> c_Orderings_Oord__class_Oless__eq(X6,X17,X16) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_577,plain,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(X6)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_578,plain,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(X6)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_579,plain,
! [X17,X16] :
( X16 != X17
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_580,plain,
! [X16,X6] :
( class_Orderings_Opreorder(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,X16,X16) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_581,plain,
! [X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_582,plain,
! [X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_583,plain,
! [X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_584,plain,
! [X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X25),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_585,plain,
! [X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X25),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_586,plain,
! [X6,X7,X4] :
( X4 = X7
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X4,X7)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_587,plain,
! [X4,X6] :
( c_Finite__Set_Ocard(X6,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X6,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff]) ).
fof(i_0_588,plain,
! [X9,X8] :
( ~ hBOOL(hAPP(c_fequal(X8),X9))
| X8 = X9 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_589,plain,
! [X4,X6] :
( ~ c_Finite__Set_Ofinite(X6,X4)
=> c_Finite__Set_Ocard(X6,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
fof(i_0_590,plain,
! [X2910,X2911,X2912,X2913,X2914,X2915,X2916,X2917] :
( ( c_member(X2916,esk33_8(X2910,X2911,X2912,X2913,X2914,X2915,X2916,X2917),X2913)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2915,X2917,X2910,X2912) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2916,X2917,X2911,X2913)
| X2912 != c_Set_Oimage(X2916,X2915,X2914,X2913)
| ~ c_Fun_Oinj__on(X2916,X2915,X2914,X2913)
| ~ class_Groups_Ocomm__monoid__add(X2917) )
& ( hAPP(X2911,esk33_8(X2910,X2911,X2912,X2913,X2914,X2915,X2916,X2917)) != hAPP(X2910,hAPP(X2914,esk33_8(X2910,X2911,X2912,X2913,X2914,X2915,X2916,X2917)))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2915,X2917,X2910,X2912) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2916,X2917,X2911,X2913)
| X2912 != c_Set_Oimage(X2916,X2915,X2914,X2913)
| ~ c_Fun_Oinj__on(X2916,X2915,X2914,X2913)
| ~ class_Groups_Ocomm__monoid__add(X2917) ) ),
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_591,plain,
! [X2919,X2920,X2921,X2922,X2923,X2924,X2925,X2926] :
( ( c_Orderings_Oord__class_Oless__eq(X2925,X2923,esk34_8(X2919,X2920,X2921,X2922,X2923,X2924,X2925,X2926))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2925,X2926,X2920,c_SetInterval_Oord__class_OatLeastLessThan(X2925,X2924,X2922)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2925,X2926,X2919,c_SetInterval_Oord__class_OatLeastLessThan(X2925,X2923,X2921))
| X2922 != X2921
| X2924 != X2923
| ~ class_Groups_Ocomm__monoid__add(X2926)
| ~ class_Orderings_Oord(X2925) )
& ( c_Orderings_Oord__class_Oless(X2925,esk34_8(X2919,X2920,X2921,X2922,X2923,X2924,X2925,X2926),X2921)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2925,X2926,X2920,c_SetInterval_Oord__class_OatLeastLessThan(X2925,X2924,X2922)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2925,X2926,X2919,c_SetInterval_Oord__class_OatLeastLessThan(X2925,X2923,X2921))
| X2922 != X2921
| X2924 != X2923
| ~ class_Groups_Ocomm__monoid__add(X2926)
| ~ class_Orderings_Oord(X2925) )
& ( hAPP(X2920,esk34_8(X2919,X2920,X2921,X2922,X2923,X2924,X2925,X2926)) != hAPP(X2919,esk34_8(X2919,X2920,X2921,X2922,X2923,X2924,X2925,X2926))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2925,X2926,X2920,c_SetInterval_Oord__class_OatLeastLessThan(X2925,X2924,X2922)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2925,X2926,X2919,c_SetInterval_Oord__class_OatLeastLessThan(X2925,X2923,X2921))
| X2922 != X2921
| X2924 != X2923
| ~ class_Groups_Ocomm__monoid__add(X2926)
| ~ class_Orderings_Oord(X2925) ) ),
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_592,plain,
! [X2495,X2496,X2497,X2498,X2499] :
( ~ c_Finite__Set_Ofolding__one__idem(X2499,X2498,X2497)
| hAPP(X2496,hAPP(hAPP(X2498,esk24_5(X2495,X2496,X2497,X2498,X2499)),esk25_5(X2495,X2496,X2497,X2498,X2499))) != hAPP(hAPP(X2498,hAPP(X2496,esk24_5(X2495,X2496,X2497,X2498,X2499))),hAPP(X2496,esk25_5(X2495,X2496,X2497,X2498,X2499)))
| ~ c_Finite__Set_Ofinite(X2499,X2495)
| X2495 = c_Orderings_Obot__class_Obot(tc_fun(X2499,tc_HOL_Obool))
| hAPP(X2496,hAPP(X2497,X2495)) = hAPP(X2497,c_Set_Oimage(X2499,X2499,X2496,X2495)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute])])]) ).
fof(i_0_593,plain,
! [X2898,X2899,X2900,X2901,X2902] :
( ( c_member(X2901,esk31_5(X2898,X2899,X2900,X2901,X2902),X2900)
| c_Orderings_Oord__class_Oless(X2902,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2901,X2902,X2899,X2900),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2901,X2902,X2898,X2900))
| X2900 = c_Orderings_Obot__class_Obot(tc_fun(X2901,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X2901,X2900)
| ~ class_Groups_Ocomm__monoid__add(X2902)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2902) )
& ( ~ c_Orderings_Oord__class_Oless(X2902,hAPP(X2899,esk31_5(X2898,X2899,X2900,X2901,X2902)),hAPP(X2898,esk31_5(X2898,X2899,X2900,X2901,X2902)))
| c_Orderings_Oord__class_Oless(X2902,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2901,X2902,X2899,X2900),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2901,X2902,X2898,X2900))
| X2900 = c_Orderings_Obot__class_Obot(tc_fun(X2901,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X2901,X2900)
| ~ class_Groups_Ocomm__monoid__add(X2902)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2902) ) ),
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_594,plain,
! [X2383,X2384,X2385,X2386,X2387,X2388,X2389,X2390] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2390,X2389,X2388,X2387,X2386,X2385)
| ~ c_Finite__Set_Ofinite(X2389,X2384)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2389,tc_HOL_Obool),X2383,X2384)
| hAPP(hAPP(X2388,hAPP(X2385,X2383)),hAPP(X2385,X2384)) = hAPP(X2385,X2384) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).
fof(i_0_595,plain,
! [X3036,X3037,X3038,X3039,X3040,X3041,X3042,X3043] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X3043,X3042,X3041,X3040,X3039,X3038)
| ~ c_Finite__Set_Ofinite(X3042,X3037)
| hAPP(X3038,c_Set_Oinsert(X3042,X3036,X3037)) = hAPP(hAPP(X3041,hAPP(X3039,X3036)),hAPP(X3038,X3037)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).
fof(i_0_596,plain,
! [X2391,X2392,X2393,X2394,X2395,X2396,X2397,X2398] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2398,X2397,X2396,X2395,X2394,X2393)
| ~ c_Finite__Set_Ofinite(X2397,X2392)
| ~ c_member(X2397,X2391,X2392)
| hAPP(hAPP(X2396,hAPP(X2394,X2391)),hAPP(X2393,X2392)) = hAPP(X2393,X2392) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).
fof(i_0_597,plain,
! [X2414,X2415,X2416,X2417,X2418,X2419,X2420] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2420,X2419,X2418,X2417,X2416,X2415)
| hAPP(hAPP(X2418,X2414),X2414) = X2414 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).
fof(i_0_598,plain,
! [X2366,X2367,X2368,X2369,X2370,X2371] :
( ( hBOOL(hAPP(hAPP(X2369,X2367),X2370))
| ~ c_member(X2371,X2370,c_SetInterval_Oord_OatLeastLessThan(X2371,X2369,X2368,X2367,X2366)) )
& ( hBOOL(hAPP(hAPP(X2368,X2370),X2366))
| ~ c_member(X2371,X2370,c_SetInterval_Oord_OatLeastLessThan(X2371,X2369,X2368,X2367,X2366)) )
& ( ~ hBOOL(hAPP(hAPP(X2369,X2367),X2370))
| ~ hBOOL(hAPP(hAPP(X2368,X2370),X2366))
| c_member(X2371,X2370,c_SetInterval_Oord_OatLeastLessThan(X2371,X2369,X2368,X2367,X2366)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])]) ).
fof(i_0_599,plain,
! [X2360,X2361,X2362,X2363,X2364,X2365] :
( ( hBOOL(hAPP(hAPP(X2362,X2361),X2364))
| ~ c_member(X2365,X2364,c_SetInterval_Oord_OgreaterThanAtMost(X2365,X2363,X2362,X2361,X2360)) )
& ( hBOOL(hAPP(hAPP(X2363,X2364),X2360))
| ~ c_member(X2365,X2364,c_SetInterval_Oord_OgreaterThanAtMost(X2365,X2363,X2362,X2361,X2360)) )
& ( ~ hBOOL(hAPP(hAPP(X2362,X2361),X2364))
| ~ hBOOL(hAPP(hAPP(X2363,X2364),X2360))
| c_member(X2365,X2364,c_SetInterval_Oord_OgreaterThanAtMost(X2365,X2363,X2362,X2361,X2360)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])]) ).
fof(i_0_600,plain,
! [X1714,X1715,X1716,X1717,X1719,X1720] :
( ( X1714 = hAPP(X1715,esk4_4(X1714,X1715,X1716,X1717))
| ~ c_member(X1716,X1714,c_Set_Oimage(X1717,X1716,X1715,c_Orderings_Otop__class_Otop(tc_fun(X1717,tc_HOL_Obool))))
| ~ c_Fun_Oinj__on(X1717,X1716,X1715,c_Orderings_Otop__class_Otop(tc_fun(X1717,tc_HOL_Obool))) )
& ( X1714 != hAPP(X1715,X1719)
| X1719 = esk4_4(X1714,X1715,X1716,X1717)
| ~ c_member(X1716,X1714,c_Set_Oimage(X1717,X1716,X1715,c_Orderings_Otop__class_Otop(tc_fun(X1717,tc_HOL_Obool))))
| ~ c_Fun_Oinj__on(X1717,X1716,X1715,c_Orderings_Otop__class_Otop(tc_fun(X1717,tc_HOL_Obool))) )
& ( X1714 = hAPP(X1715,esk5_5(X1714,X1715,X1716,X1717,X1720))
| X1714 != hAPP(X1715,X1720)
| c_member(X1716,X1714,c_Set_Oimage(X1717,X1716,X1715,c_Orderings_Otop__class_Otop(tc_fun(X1717,tc_HOL_Obool))))
| ~ c_Fun_Oinj__on(X1717,X1716,X1715,c_Orderings_Otop__class_Otop(tc_fun(X1717,tc_HOL_Obool))) )
& ( esk5_5(X1714,X1715,X1716,X1717,X1720) != X1720
| X1714 != hAPP(X1715,X1720)
| c_member(X1716,X1714,c_Set_Oimage(X1717,X1716,X1715,c_Orderings_Otop__class_Otop(tc_fun(X1717,tc_HOL_Obool))))
| ~ c_Fun_Oinj__on(X1717,X1716,X1715,c_Orderings_Otop__class_Otop(tc_fun(X1717,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_601,plain,
! [X2259,X2260,X2261,X2262,X2263,X2265,X2266,X2267,X2268,X2269,X2270] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2261,tc_HOL_Obool),esk19_5(X2259,X2260,X2261,X2262,X2263),X2259)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2263,tc_HOL_Obool),X2262,c_Set_Oimage(X2261,X2263,X2260,X2259)) )
& ( X2262 = c_Set_Oimage(X2261,X2263,X2260,esk19_5(X2259,X2260,X2261,X2262,X2263))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2263,tc_HOL_Obool),X2262,c_Set_Oimage(X2261,X2263,X2260,X2259)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2267,tc_HOL_Obool),X2270,X2265)
| X2268 != c_Set_Oimage(X2267,X2269,X2266,X2270)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2269,tc_HOL_Obool),X2268,c_Set_Oimage(X2267,X2269,X2266,X2265)) ) ),
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_602,plain,
! [X1751,X1752,X1753,X1754,X1755] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1753,X1754),X1752,X1751)
| c_Orderings_Oord__class_Oless__eq(X1754,hAPP(X1752,X1755),hAPP(X1751,X1755))
| ~ class_Orderings_Oord(X1754) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1754,hAPP(X1752,esk6_4(X1751,X1752,X1753,X1754)),hAPP(X1751,esk6_4(X1751,X1752,X1753,X1754)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X1753,X1754),X1752,X1751)
| ~ class_Orderings_Oord(X1754) ) ),
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_603,plain,
! [X2979,X2980,X2981,X2982,X2983] :
( ~ class_Groups_Ocomm__monoid__add(X2983)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2982,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2981,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2983,X2980,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2982,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2981,X2979))) = c_Groups_Oplus__class_Oplus(X2983,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2983,X2980,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2982,X2981)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2983,X2980,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2981,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2981,X2979)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat])]) ).
fof(i_0_604,plain,
! [X1679,X1680,X1681,X1682,X1683,X1684] :
( ~ c_Fun_Oinj__on(X1684,X1683,X1682,X1681)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1683,tc_HOL_Obool),c_Set_Oimage(X1684,X1683,X1682,X1681),X1680)
| ~ c_Fun_Oinj__on(X1683,X1684,X1679,X1680)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1684,tc_HOL_Obool),c_Set_Oimage(X1683,X1684,X1679,X1680),X1681)
| ~ c_Finite__Set_Ofinite(X1684,X1681)
| ~ c_Finite__Set_Ofinite(X1683,X1680)
| c_Finite__Set_Ocard(X1684,X1681) = c_Finite__Set_Ocard(X1683,X1680) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).
fof(i_0_605,plain,
! [X1955,X1956,X1957,X1958,X1959,X1960] :
( ~ c_Fun_Oinj__on(X1960,X1959,X1958,X1957)
| ~ c_member(X1959,X1956,c_Set_Oimage(X1960,X1959,X1958,X1957))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1960,tc_HOL_Obool),X1957,X1955)
| c_member(X1960,hAPP(c_Fun_Othe__inv__into(X1960,X1959,X1957,X1958),X1956),X1955) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__into])]) ).
fof(i_0_606,plain,
! [X1999,X2000,X2001,X2002,X2003] :
( ~ c_Fun_Oinj__on(X2003,X2002,X2001,X2000)
| ~ c_member(X2002,X1999,c_Set_Oimage(X2003,X2002,X2001,X2000))
| hAPP(X2001,hAPP(c_Fun_Othe__inv__into(X2003,X2002,X2000,X2001),X1999)) = X1999 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f])]) ).
fof(i_0_607,plain,
! [X1704,X1705,X1706,X1707,X1708] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1707,tc_HOL_Obool),c_Set_Oimage(X1708,X1707,X1706,X1705),c_Set_Oimage(X1708,X1707,X1706,X1704))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X1708,tc_HOL_Obool),X1705,X1704)
| ~ c_Fun_Oinj__on(X1708,X1707,X1706,c_Orderings_Otop__class_Otop(tc_fun(X1708,tc_HOL_Obool))) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1708,tc_HOL_Obool),X1705,X1704)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X1707,tc_HOL_Obool),c_Set_Oimage(X1708,X1707,X1706,X1705),c_Set_Oimage(X1708,X1707,X1706,X1704))
| ~ c_Fun_Oinj__on(X1708,X1707,X1706,c_Orderings_Otop__class_Otop(tc_fun(X1708,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_608,plain,
! [X1700,X1701,X1702,X1703] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(X1703,c_Set_Oimage(X1702,X1703,X1701,X1700)),c_Finite__Set_Ocard(X1702,X1700))
| ~ c_Fun_Oinj__on(X1702,X1703,X1701,X1700) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_519])]) ).
fof(i_0_609,plain,
! [X2049,X2050,X2051,X2052,X2053,X2055] :
( ( ~ c_Fun_Oinj__on(X2051,X2050,X2053,X2052)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2050,tc_HOL_Obool),c_Set_Oimage(X2051,X2050,X2053,X2052),X2049)
| c_Set_Oimage(X2050,X2051,esk8_4(X2049,X2050,X2051,X2052),X2049) = X2052
| X2052 = c_Orderings_Obot__class_Obot(tc_fun(X2051,tc_HOL_Obool)) )
& ( c_Fun_Oinj__on(X2051,X2050,esk9_4(X2049,X2050,X2051,X2052),X2052)
| c_Set_Oimage(X2050,X2051,X2055,X2049) != X2052
| X2052 = c_Orderings_Obot__class_Obot(tc_fun(X2051,tc_HOL_Obool)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2050,tc_HOL_Obool),c_Set_Oimage(X2051,X2050,esk9_4(X2049,X2050,X2051,X2052),X2052),X2049)
| c_Set_Oimage(X2050,X2051,X2055,X2049) != X2052
| X2052 = c_Orderings_Obot__class_Obot(tc_fun(X2051,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_610,plain,
! [X2859,X2860,X2861,X2862,X2863] :
( ~ class_Groups_Ocomm__monoid__add(X2863)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2862,X2861)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2861,X2860)
| c_Groups_Oplus__class_Oplus(X2863,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2863,X2859,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2862,X2861)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2863,X2859,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2861,X2860))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2863,X2859,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2862,X2860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl])]) ).
fof(i_0_611,plain,
! [X2025,X2026,X2027,X2028,X2029] :
( ( ~ c_Fun_Oinj__on(X2028,X2026,X2029,X2027)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2026,tc_HOL_Obool),c_Set_Oimage(X2028,X2026,X2029,X2027),X2025)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2028,X2027),c_Finite__Set_Ocard(X2026,X2025))
| ~ c_Finite__Set_Ofinite(X2026,X2025)
| ~ c_Finite__Set_Ofinite(X2028,X2027) )
& ( c_Fun_Oinj__on(X2028,X2026,esk7_4(X2025,X2026,X2027,X2028),X2027)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2028,X2027),c_Finite__Set_Ocard(X2026,X2025))
| ~ c_Finite__Set_Ofinite(X2026,X2025)
| ~ c_Finite__Set_Ofinite(X2028,X2027) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2026,tc_HOL_Obool),c_Set_Oimage(X2028,X2026,esk7_4(X2025,X2026,X2027,X2028),X2027),X2025)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2028,X2027),c_Finite__Set_Ocard(X2026,X2025))
| ~ c_Finite__Set_Ofinite(X2026,X2025)
| ~ c_Finite__Set_Ofinite(X2028,X2027) ) ),
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_612,plain,
! [X1686,X1687,X1688,X1689] :
( ~ c_Fun_Oinj__on(X1689,X1688,X1687,X1686)
| c_Set_Oimage(X1688,X1689,c_Fun_Othe__inv__into(X1689,X1688,X1686,X1687),c_Set_Oimage(X1689,X1688,X1687,X1686)) = X1686 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])]) ).
fof(i_0_613,plain,
! [X1690,X1691,X1692,X1693] :
( ~ c_Fun_Oinj__on(X1693,X1692,X1691,X1690)
| c_Fun_Oinj__on(X1692,X1693,c_Fun_Othe__inv__into(X1693,X1692,X1690,X1691),c_Set_Oimage(X1693,X1692,X1691,X1690)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into])]) ).
fof(i_0_614,plain,
! [X2101,X2102,X2103,X2104,X2105] :
( ~ c_Fun_Oinj__on(X2105,X2104,X2103,X2102)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2105,tc_HOL_Obool),X2101,X2102)
| c_Orderings_Oord__class_Oless(tc_fun(X2104,tc_HOL_Obool),c_Set_Oimage(X2105,X2104,X2103,X2101),c_Set_Oimage(X2105,X2104,X2103,X2102)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).
fof(i_0_615,plain,
! [X2022,X2023,X2024] :
( ~ c_Finite__Set_Ofinite(X2024,X2023)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2024,tc_HOL_Obool),c_Set_Oimage(X2024,X2024,X2022,X2023),X2023)
| ~ c_Fun_Oinj__on(X2024,X2024,X2022,X2023)
| c_Set_Oimage(X2024,X2024,X2022,X2023) = X2023 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).
fof(i_0_616,plain,
! [X2905,X2906,X2907,X2908] :
( ( c_member(X2908,esk32_4(X2905,X2906,X2907,X2908),X2906)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2908,tc_Nat_Onat,X2907,X2906) != hAPP(c_Nat_OSuc,X2905) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(X2907,esk32_4(X2905,X2906,X2907,X2908)))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2908,tc_Nat_Onat,X2907,X2906) != hAPP(c_Nat_OSuc,X2905) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__SucD])])])]) ).
fof(i_0_617,plain,
! [X1709,X1710,X1711,X1712,X1713] :
( ( ~ c_member(X1712,hAPP(X1711,X1710),c_Set_Oimage(X1713,X1712,X1711,X1709))
| c_member(X1713,X1710,X1709)
| ~ c_Fun_Oinj__on(X1713,X1712,X1711,c_Orderings_Otop__class_Otop(tc_fun(X1713,tc_HOL_Obool))) )
& ( ~ c_member(X1713,X1710,X1709)
| c_member(X1712,hAPP(X1711,X1710),c_Set_Oimage(X1713,X1712,X1711,X1709))
| ~ c_Fun_Oinj__on(X1713,X1712,X1711,c_Orderings_Otop__class_Otop(tc_fun(X1713,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_618,plain,
! [X2006,X2007,X2008,X2009,X2010] :
( ~ c_Fun_Oinj__on(X2010,X2009,X2008,X2007)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2009,tc_HOL_Obool),c_Set_Oimage(X2010,X2009,X2008,X2007),X2006)
| ~ c_Finite__Set_Ofinite(X2009,X2006)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2010,X2007),c_Finite__Set_Ocard(X2009,X2006)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).
fof(i_0_619,plain,
! [X2220,X2221,X2222,X2223,X2224,X2226,X2227,X2228,X2229,X2230,X2231] :
( ( c_member(X2222,esk18_4(X2220,X2221,X2222,X2223),X2220)
| ~ c_member(X2224,X2223,c_Set_Oimage(X2222,X2224,X2221,X2220)) )
& ( X2223 = hAPP(X2221,esk18_4(X2220,X2221,X2222,X2223))
| ~ c_member(X2224,X2223,c_Set_Oimage(X2222,X2224,X2221,X2220)) )
& ( ~ c_member(X2228,X2230,X2226)
| X2229 != hAPP(X2227,X2230)
| c_member(X2231,X2229,c_Set_Oimage(X2228,X2231,X2227,X2226)) ) ),
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_620,plain,
! [X3183,X3184,X3185] :
( ~ c_Finite__Set_Ofinite(X3185,X3184)
| ~ c_member(X3185,X3183,X3184)
| c_Finite__Set_Ocard(X3185,X3184) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(X3185,c_Groups_Ominus__class_Ominus(tc_fun(X3185,tc_HOL_Obool),X3184,c_Set_Oinsert(X3185,X3183,c_Orderings_Obot__class_Obot(tc_fun(X3185,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oremove])]) ).
fof(i_0_621,plain,
! [X2975,X2976,X2977,X2978] :
( ~ class_Groups_Ocomm__monoid__add(X2978)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2977,X2976)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2978,X2975,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2977,X2976)) = c_Groups_Oplus__class_Oplus(X2978,hAPP(X2975,X2977),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2978,X2975,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2977),X2976))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc])]) ).
fof(i_0_622,plain,
! [X2867,X2868,X2869,X2870] :
( ~ class_Groups_Ocomm__monoid__add(X2870)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2869,X2868)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2870,X2867,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2869,X2868)) = c_Groups_Oplus__class_Oplus(X2870,hAPP(X2867,X2869),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2870,X2867,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2869),X2868))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc])]) ).
fof(i_0_623,plain,
! [X2928,X2929,X2930,X2931] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2930),X2929)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2931,X2928,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2929,hAPP(c_Nat_OSuc,X2930))) = c_Groups_Ozero__class_Ozero(X2931)
| ~ class_Groups_Ocomm__monoid__add(X2931) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2930),X2929)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2931,X2928,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2929,hAPP(c_Nat_OSuc,X2930))) = c_Groups_Oplus__class_Oplus(X2931,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2931,X2928,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2929,X2930)),hAPP(X2928,hAPP(c_Nat_OSuc,X2930)))
| ~ class_Groups_Ocomm__monoid__add(X2931) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_520])])]) ).
fof(i_0_624,plain,
! [X1629,X1630,X1631,X1632,X1633,X1634,X1635,X1636,X1637,X1638] :
( ( ~ c_Fun_Oinj__on(X1632,X1631,X1630,X1629)
| ~ c_member(X1632,X1633,X1629)
| ~ c_member(X1632,X1634,X1629)
| hAPP(X1630,X1633) != hAPP(X1630,X1634)
| X1633 = X1634 )
& ( c_member(X1638,esk2_4(X1635,X1636,X1637,X1638),X1635)
| c_Fun_Oinj__on(X1638,X1637,X1636,X1635) )
& ( c_member(X1638,esk3_4(X1635,X1636,X1637,X1638),X1635)
| c_Fun_Oinj__on(X1638,X1637,X1636,X1635) )
& ( hAPP(X1636,esk2_4(X1635,X1636,X1637,X1638)) = hAPP(X1636,esk3_4(X1635,X1636,X1637,X1638))
| c_Fun_Oinj__on(X1638,X1637,X1636,X1635) )
& ( esk2_4(X1635,X1636,X1637,X1638) != esk3_4(X1635,X1636,X1637,X1638)
| c_Fun_Oinj__on(X1638,X1637,X1636,X1635) ) ),
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_625,plain,
! [X1609,X1610,X1611,X1612,X1613] :
( ( c_Set_Oimage(X1613,X1612,X1611,X1610) != c_Set_Oimage(X1613,X1612,X1611,X1609)
| X1610 = X1609
| ~ c_Fun_Oinj__on(X1613,X1612,X1611,c_Orderings_Otop__class_Otop(tc_fun(X1613,tc_HOL_Obool))) )
& ( X1610 != X1609
| c_Set_Oimage(X1613,X1612,X1611,X1610) = c_Set_Oimage(X1613,X1612,X1611,X1609)
| ~ c_Fun_Oinj__on(X1613,X1612,X1611,c_Orderings_Otop__class_Otop(tc_fun(X1613,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_626,plain,
! [X2855,X2856,X2857,X2858] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2857,X2856)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2858,X2855,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2856,hAPP(c_Nat_OSuc,X2857))) = c_Groups_Ozero__class_Ozero(X2858)
| ~ class_Groups_Ocomm__monoid__add(X2858) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2857,X2856)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2858,X2855,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2856,hAPP(c_Nat_OSuc,X2857))) = c_Groups_Oplus__class_Oplus(X2858,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2858,X2855,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2856,X2857)),hAPP(X2855,X2857))
| ~ class_Groups_Ocomm__monoid__add(X2858) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_521])])]) ).
fof(i_0_627,plain,
! [X2884,X2885,X2886,X2888,X2889] :
( ( c_member(X2886,esk29_3(X2884,X2885,X2886),X2885)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2886,tc_Nat_Onat,X2884,X2885) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Finite__Set_Ofinite(X2886,X2885) )
& ( hAPP(X2884,esk29_3(X2884,X2885,X2886)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2886,tc_Nat_Onat,X2884,X2885) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Finite__Set_Ofinite(X2886,X2885) )
& ( ~ c_member(X2886,X2888,X2885)
| esk29_3(X2884,X2885,X2886) = X2888
| hAPP(X2884,X2888) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2886,tc_Nat_Onat,X2884,X2885) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Finite__Set_Ofinite(X2886,X2885) )
& ( c_member(X2886,esk30_4(X2884,X2885,X2886,X2889),X2885)
| ~ c_member(X2886,X2889,X2885)
| hAPP(X2884,X2889) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2886,tc_Nat_Onat,X2884,X2885) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Finite__Set_Ofinite(X2886,X2885) )
& ( X2889 != esk30_4(X2884,X2885,X2886,X2889)
| ~ c_member(X2886,X2889,X2885)
| hAPP(X2884,X2889) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2886,tc_Nat_Onat,X2884,X2885) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Finite__Set_Ofinite(X2886,X2885) )
& ( hAPP(X2884,esk30_4(X2884,X2885,X2886,X2889)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_member(X2886,X2889,X2885)
| hAPP(X2884,X2889) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2886,tc_Nat_Onat,X2884,X2885) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Finite__Set_Ofinite(X2886,X2885) ) ),
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_628,plain,
! [X1661,X1662,X1663,X1664] :
( ~ c_Finite__Set_Ofinite(X1664,c_Set_Oimage(X1663,X1664,X1662,X1661))
| ~ c_Fun_Oinj__on(X1663,X1664,X1662,X1661)
| c_Finite__Set_Ofinite(X1663,X1661) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
fof(i_0_629,plain,
! [X2254,X2255,X2256,X2257,X2258] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2258,tc_HOL_Obool),X2257,X2256)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2255,tc_HOL_Obool),c_Set_Oimage(X2258,X2255,X2254,X2257),c_Set_Oimage(X2258,X2255,X2254,X2256)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_630,plain,
! [X2997,X2998,X2999,X3001,X3002] :
( ( c_member(X2999,esk39_3(X2997,X2998,X2999),X2998)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2999,tc_Nat_Onat,X2997,X2998) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2999,X2998) )
& ( hAPP(X2997,esk39_3(X2997,X2998,X2999)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2999,tc_Nat_Onat,X2997,X2998) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2999,X2998) )
& ( ~ c_member(X2999,X3001,X2998)
| esk39_3(X2997,X2998,X2999) = X3001
| hAPP(X2997,X3001) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2999,tc_Nat_Onat,X2997,X2998) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2999,X2998) )
& ( c_member(X2999,esk40_4(X2997,X2998,X2999,X3002),X2998)
| ~ c_member(X2999,X3002,X2998)
| hAPP(X2997,X3002) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2999,tc_Nat_Onat,X2997,X2998) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2999,X2998) )
& ( X3002 != esk40_4(X2997,X2998,X2999,X3002)
| ~ c_member(X2999,X3002,X2998)
| hAPP(X2997,X3002) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2999,tc_Nat_Onat,X2997,X2998) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2999,X2998) )
& ( hAPP(X2997,esk40_4(X2997,X2998,X2999,X3002)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_member(X2999,X3002,X2998)
| hAPP(X2997,X3002) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2999,tc_Nat_Onat,X2997,X2998) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2999,X2998) ) ),
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_631,hypothesis,
! [X3207] :
( ~ c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X3207,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
| c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X3207,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))
| v_thesis____ ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])]) ).
fof(i_0_632,plain,
! [X2019,X2020,X2021] :
( ~ c_Finite__Set_Ofinite(X2021,X2020)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2021,tc_HOL_Obool),X2020,c_Set_Oimage(X2021,X2021,X2019,X2020))
| c_Fun_Oinj__on(X2021,X2021,X2019,X2020) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).
fof(i_0_633,plain,
! [X1722,X1723,X1724,X1725] :
( ~ c_Finite__Set_Ofinite(X1725,X1724)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1723,c_Set_Oimage(X1725,X1723,X1722,X1724)),c_Finite__Set_Ocard(X1725,X1724)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).
fof(i_0_634,plain,
! [X1694,X1695,X1696,X1697] :
( ~ c_Fun_Oinj__on(X1697,X1696,X1695,c_Orderings_Otop__class_Otop(tc_fun(X1697,tc_HOL_Obool)))
| hAPP(c_Fun_Othe__inv__into(X1697,X1696,c_Orderings_Otop__class_Otop(tc_fun(X1697,tc_HOL_Obool)),X1695),hAPP(X1695,X1694)) = X1694 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__f__f])]) ).
fof(i_0_635,plain,
! [X1671,X1672,X1673,X1674] :
( ~ c_Finite__Set_Ofinite(X1674,X1673)
| c_Finite__Set_Ocard(X1672,c_Set_Oimage(X1674,X1672,X1671,X1673)) != c_Finite__Set_Ocard(X1674,X1673)
| c_Fun_Oinj__on(X1674,X1672,X1671,X1673) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).
fof(i_0_636,plain,
! [X1675,X1676,X1677,X1678] :
( ( ~ c_Fun_Oinj__on(X1678,X1676,X1675,X1677)
| c_Finite__Set_Ocard(X1676,c_Set_Oimage(X1678,X1676,X1675,X1677)) = c_Finite__Set_Ocard(X1678,X1677)
| ~ c_Finite__Set_Ofinite(X1678,X1677) )
& ( c_Finite__Set_Ocard(X1676,c_Set_Oimage(X1678,X1676,X1675,X1677)) != c_Finite__Set_Ocard(X1678,X1677)
| c_Fun_Oinj__on(X1678,X1676,X1675,X1677)
| ~ c_Finite__Set_Ofinite(X1678,X1677) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).
fof(i_0_637,plain,
! [X3153,X3154,X3155,X3156,X3157] :
( ~ class_Groups_Ocomm__monoid__add(X3157)
| ~ c_Finite__Set_Ofinite(X3156,X3155)
| c_member(X3156,X3154,X3155)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3156,X3157,X3153,c_Set_Oinsert(X3156,X3154,X3155)) = c_Groups_Oplus__class_Oplus(X3157,hAPP(X3153,X3154),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3156,X3157,X3153,X3155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_522])]) ).
fof(i_0_638,plain,
! [X3148,X3149,X3150,X3151,X3152] :
( ~ class_Groups_Ocomm__monoid__add(X3152)
| ~ c_Finite__Set_Ofinite(X3151,X3150)
| c_member(X3151,X3149,X3150)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3151,X3152,X3148,c_Set_Oinsert(X3151,X3149,X3150)) = c_Groups_Oplus__class_Oplus(X3152,hAPP(X3148,X3149),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3151,X3152,X3148,X3150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_523])]) ).
fof(i_0_639,plain,
! [X1950,X1951,X1952,X1953,X1954] :
( ~ c_Fun_Oinj__on(X1954,X1953,X1952,X1951)
| ~ c_member(X1954,X1950,X1951)
| hAPP(c_Fun_Othe__inv__into(X1954,X1953,X1951,X1952),hAPP(X1952,X1950)) = X1950 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f])]) ).
fof(i_0_640,plain,
! [X1944,X1945,X1946,X1947,X1948,X1949] :
( ~ c_Fun_Oinj__on(X1949,X1948,X1947,X1946)
| hAPP(X1947,X1945) != X1944
| ~ c_member(X1949,X1945,X1946)
| hAPP(c_Fun_Othe__inv__into(X1949,X1948,X1946,X1947),X1944) = X1945 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq])]) ).
fof(i_0_641,plain,
! [X2587,X2588] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X2588,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2587,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2587,c_Finite__Set_Ocard(tc_Nat_Onat,X2588))))
| X2588 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2587,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2587,c_Finite__Set_Ocard(tc_Nat_Onat,X2588))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).
fof(i_0_642,plain,
! [X2351,X2352,X2353,X2354,X2355] :
( ( hBOOL(hAPP(hAPP(X2353,X2352),X2354))
| ~ c_member(X2355,X2354,c_SetInterval_Oord_OgreaterThanLessThan(X2355,X2353,X2352,X2351)) )
& ( hBOOL(hAPP(hAPP(X2353,X2354),X2351))
| ~ c_member(X2355,X2354,c_SetInterval_Oord_OgreaterThanLessThan(X2355,X2353,X2352,X2351)) )
& ( ~ hBOOL(hAPP(hAPP(X2353,X2352),X2354))
| ~ hBOOL(hAPP(hAPP(X2353,X2354),X2351))
| c_member(X2355,X2354,c_SetInterval_Oord_OgreaterThanLessThan(X2355,X2353,X2352,X2351)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])]) ).
fof(i_0_643,plain,
! [X2346,X2347,X2348,X2349,X2350] :
( ( hBOOL(hAPP(hAPP(X2348,X2347),X2349))
| ~ c_member(X2350,X2349,c_SetInterval_Oord_OatLeastAtMost(X2350,X2348,X2347,X2346)) )
& ( hBOOL(hAPP(hAPP(X2348,X2349),X2346))
| ~ c_member(X2350,X2349,c_SetInterval_Oord_OatLeastAtMost(X2350,X2348,X2347,X2346)) )
& ( ~ hBOOL(hAPP(hAPP(X2348,X2347),X2349))
| ~ hBOOL(hAPP(hAPP(X2348,X2349),X2346))
| c_member(X2350,X2349,c_SetInterval_Oord_OatLeastAtMost(X2350,X2348,X2347,X2346)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])]) ).
fof(i_0_644,plain,
! [X2011,X2012,X2013,X2014,X2015] :
( ~ c_Finite__Set_Ofinite(X2015,X2014)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2013,tc_HOL_Obool),X2012,c_Set_Oimage(X2015,X2013,X2011,X2014))
| c_Finite__Set_Ofinite(X2013,X2012) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
fof(i_0_645,plain,
! [X3077,X3078,X3079,X3080,X3081] : c_Set_Oimage(X3081,X3080,X3079,c_Set_Oinsert(X3081,X3078,X3077)) = c_Set_Oinsert(X3080,hAPP(X3079,X3078),c_Set_Oimage(X3081,X3080,X3079,X3077)),
inference(variable_rename,[status(thm)],[fact_image__insert]) ).
fof(i_0_646,plain,
! [X1667,X1668] :
( ~ c_Finite__Set_Ofinite(X1668,c_Orderings_Otop__class_Otop(tc_fun(X1668,tc_HOL_Obool)))
| c_Set_Oimage(X1668,X1668,X1667,c_Orderings_Otop__class_Otop(tc_fun(X1668,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X1668,tc_HOL_Obool))
| c_Fun_Oinj__on(X1668,X1668,X1667,c_Orderings_Otop__class_Otop(tc_fun(X1668,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).
fof(i_0_647,plain,
! [X1605,X1606,X1607,X1608] :
( ~ c_Fun_Oinj__on(X1608,X1607,X1606,X1605)
| c_Finite__Set_Ocard(X1607,c_Set_Oimage(X1608,X1607,X1606,X1605)) = c_Finite__Set_Ocard(X1608,X1605) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).
fof(i_0_648,plain,
! [X3069,X3070,X3071,X3072,X3073] :
( ~ c_member(X3073,X3072,X3071)
| c_Set_Oinsert(X3070,hAPP(X3069,X3072),c_Set_Oimage(X3073,X3070,X3069,X3071)) = c_Set_Oimage(X3073,X3070,X3069,X3071) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).
fof(i_0_649,plain,
! [X1669,X1670] :
( ~ c_Finite__Set_Ofinite(X1670,c_Orderings_Otop__class_Otop(tc_fun(X1670,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X1670,X1670,X1669,c_Orderings_Otop__class_Otop(tc_fun(X1670,tc_HOL_Obool)))
| c_Set_Oimage(X1670,X1670,X1669,c_Orderings_Otop__class_Otop(tc_fun(X1670,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1670,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
fof(i_0_650,plain,
! [X2515,X2516,X2517,X2518] :
( ( c_Finite__Set_Ofinite(X2518,X2516)
| ~ c_Finite__Set_Ofinite(tc_sum(X2518,X2517),c_Sum__Type_OPlus(X2518,X2517,X2516,X2515)) )
& ( c_Finite__Set_Ofinite(X2517,X2515)
| ~ c_Finite__Set_Ofinite(tc_sum(X2518,X2517),c_Sum__Type_OPlus(X2518,X2517,X2516,X2515)) )
& ( ~ c_Finite__Set_Ofinite(X2518,X2516)
| ~ c_Finite__Set_Ofinite(X2517,X2515)
| c_Finite__Set_Ofinite(tc_sum(X2518,X2517),c_Sum__Type_OPlus(X2518,X2517,X2516,X2515)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).
fof(i_0_651,plain,
! [X2523,X2524,X2525,X2526] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2526,X2525),c_Sum__Type_OPlus(X2526,X2525,X2524,X2523))
| c_Finite__Set_Ofinite(X2526,X2524) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).
fof(i_0_652,plain,
! [X2502,X2503,X2504,X2505] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2505,X2504),c_Sum__Type_OPlus(X2505,X2504,X2503,X2502))
| c_Finite__Set_Ofinite(X2504,X2502) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).
fof(i_0_653,plain,
! [X3117,X3118,X3119,X3120,X3121] :
( ( X3120 = X3117
| X3120 = X3118
| c_Set_Oinsert(X3121,X3120,c_Set_Oinsert(X3121,X3119,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) != c_Set_Oinsert(X3121,X3118,c_Set_Oinsert(X3121,X3117,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) )
& ( X3119 = X3118
| X3120 = X3118
| c_Set_Oinsert(X3121,X3120,c_Set_Oinsert(X3121,X3119,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) != c_Set_Oinsert(X3121,X3118,c_Set_Oinsert(X3121,X3117,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) )
& ( X3120 = X3117
| X3119 = X3117
| c_Set_Oinsert(X3121,X3120,c_Set_Oinsert(X3121,X3119,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) != c_Set_Oinsert(X3121,X3118,c_Set_Oinsert(X3121,X3117,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) )
& ( X3119 = X3118
| X3119 = X3117
| c_Set_Oinsert(X3121,X3120,c_Set_Oinsert(X3121,X3119,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) != c_Set_Oinsert(X3121,X3118,c_Set_Oinsert(X3121,X3117,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) )
& ( X3120 != X3118
| X3119 != X3117
| c_Set_Oinsert(X3121,X3120,c_Set_Oinsert(X3121,X3119,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) = c_Set_Oinsert(X3121,X3118,c_Set_Oinsert(X3121,X3117,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) )
& ( X3120 != X3117
| X3119 != X3118
| c_Set_Oinsert(X3121,X3120,c_Set_Oinsert(X3121,X3119,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) = c_Set_Oinsert(X3121,X3118,c_Set_Oinsert(X3121,X3117,c_Orderings_Obot__class_Obot(tc_fun(X3121,tc_HOL_Obool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])]) ).
fof(i_0_654,plain,
! [X2864,X2865,X2866] :
( ~ class_Groups_Ocomm__monoid__add(X2866)
| hAPP(X2865,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X2866)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2866,X2865,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2864)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2866,X2865,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2864)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])]) ).
fof(i_0_655,plain,
! [X3004,X3005] :
( ( ~ c_Orderings_Oord__class_Oless(X3005,c_Groups_Oplus__class_Oplus(X3005,c_Groups_Oplus__class_Oplus(X3005,c_Groups_Oone__class_Oone(X3005),X3004),X3004),c_Groups_Ozero__class_Ozero(X3005))
| c_Orderings_Oord__class_Oless(X3005,X3004,c_Groups_Ozero__class_Ozero(X3005))
| ~ c_member(X3005,X3004,c_Int_Oring__1__class_OInts(X3005))
| ~ class_Rings_Olinordered__idom(X3005) )
& ( ~ c_Orderings_Oord__class_Oless(X3005,X3004,c_Groups_Ozero__class_Ozero(X3005))
| c_Orderings_Oord__class_Oless(X3005,c_Groups_Oplus__class_Oplus(X3005,c_Groups_Oplus__class_Oplus(X3005,c_Groups_Oone__class_Oone(X3005),X3004),X3004),c_Groups_Ozero__class_Ozero(X3005))
| ~ c_member(X3005,X3004,c_Int_Oring__1__class_OInts(X3005))
| ~ class_Rings_Olinordered__idom(X3005) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).
fof(i_0_656,plain,
! [X2968,X2969] :
( hAPP(X2969,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X2969,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2968)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X2969,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2968)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0])]) ).
fof(i_0_657,plain,
! [X1994,X1995,X1996,X1997,X1998] :
( ~ c_Fun_Oinj__on(X1998,X1997,X1996,X1995)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1998,tc_HOL_Obool),X1994,X1995)
| c_Fun_Oinj__on(X1998,X1997,X1996,X1994) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).
fof(i_0_658,plain,
! [X2808,X2809,X2810,X2811] :
( ~ c_Finite__Set_Ofinite(X2811,X2810)
| ~ c_Finite__Set_Ofinite(X2809,X2808)
| c_Finite__Set_Ocard(tc_sum(X2811,X2809),c_Sum__Type_OPlus(X2811,X2809,X2810,X2808)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(X2811,X2810),c_Finite__Set_Ocard(X2809,X2808)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).
fof(i_0_659,plain,
! [X2533,X2534,X2535,X2536] :
( ( ~ c_Finite__Set_Ofinite(X2536,X2535)
| ~ c_Finite__Set_Ofinite(X2534,X2533)
| c_Finite__Set_Ocard(tc_sum(X2536,X2534),c_Sum__Type_OPlus(X2536,X2534,X2535,X2533)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(X2536,X2535),c_Finite__Set_Ocard(X2534,X2533)) )
& ( c_Finite__Set_Ofinite(X2536,X2535)
| c_Finite__Set_Ocard(tc_sum(X2536,X2534),c_Sum__Type_OPlus(X2536,X2534,X2535,X2533)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X2534,X2533)
| c_Finite__Set_Ocard(tc_sum(X2536,X2534),c_Sum__Type_OPlus(X2536,X2534,X2535,X2533)) = 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_660,plain,
! [X2304,X2305,X2306,X2307] : c_member(X2307,hAPP(X2306,X2305),c_Set_Oimage(X2304,X2307,X2306,c_Orderings_Otop__class_Otop(tc_fun(X2304,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(i_0_661,plain,
! [X2299,X2300,X2301,X2302,X2303] :
( X2303 != hAPP(X2302,X2301)
| c_member(X2300,X2303,c_Set_Oimage(X2299,X2300,X2302,c_Orderings_Otop__class_Otop(tc_fun(X2299,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
fof(i_0_662,plain,
! [X2970,X2971,X2972,X2973,X2974] :
( ( c_Orderings_Oord__class_Oless__eq(X2974,X2971,X2973)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,X2973,X2972)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2974,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2973,X2972),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2971,X2970))
| ~ class_Orderings_Oorder(X2974) )
& ( c_Orderings_Oord__class_Oless__eq(X2974,X2972,X2970)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,X2973,X2972)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2974,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2973,X2972),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2971,X2970))
| ~ class_Orderings_Oorder(X2974) )
& ( c_Orderings_Oord__class_Oless(X2974,X2971,X2973)
| c_Orderings_Oord__class_Oless(X2974,X2972,X2970)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,X2973,X2972)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2974,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2973,X2972),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2971,X2970))
| ~ class_Orderings_Oorder(X2974) )
& ( c_Orderings_Oord__class_Oless__eq(X2974,X2971,X2970)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2974,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2973,X2972),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2971,X2970))
| ~ class_Orderings_Oorder(X2974) )
& ( c_Orderings_Oord__class_Oless__eq(X2974,X2973,X2972)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,X2971,X2970)
| c_Orderings_Oord__class_Oless(tc_fun(X2974,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2973,X2972),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2971,X2970))
| ~ class_Orderings_Oorder(X2974) )
& ( ~ c_Orderings_Oord__class_Oless(X2974,X2971,X2973)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,X2971,X2973)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,X2972,X2970)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,X2971,X2970)
| c_Orderings_Oord__class_Oless(tc_fun(X2974,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2973,X2972),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2971,X2970))
| ~ class_Orderings_Oorder(X2974) )
& ( ~ c_Orderings_Oord__class_Oless(X2974,X2972,X2970)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,X2971,X2973)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,X2972,X2970)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,X2971,X2970)
| c_Orderings_Oord__class_Oless(tc_fun(X2974,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2973,X2972),c_SetInterval_Oord__class_OatLeastAtMost(X2974,X2971,X2970))
| ~ class_Orderings_Oorder(X2974) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])])]) ).
fof(i_0_663,plain,
! [X2215,X2216,X2217,X2218,X2219] :
( ~ c_member(X2219,X2218,X2217)
| c_member(X2216,hAPP(X2215,X2218),c_Set_Oimage(X2219,X2216,X2215,X2217)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_664,plain,
! [X2035,X2036,X2037,X2038,X2039,X2040] :
( X2040 != hAPP(X2039,X2038)
| ~ c_member(X2037,X2038,X2036)
| c_member(X2035,X2040,c_Set_Oimage(X2037,X2035,X2039,X2036)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_665,plain,
! [X2209,X2210,X2211,X2212,X2213,X2214] :
( ~ c_member(X2214,X2213,X2212)
| X2211 != hAPP(X2210,X2213)
| c_member(X2209,X2211,c_Set_Oimage(X2214,X2209,X2210,X2212)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_666,plain,
! [X1982,X1983,X1984,X1985,X1986,X1987] :
( ( hAPP(X1985,X1983) != hAPP(X1985,X1982)
| X1983 = X1982
| ~ c_member(X1987,X1982,X1984)
| ~ c_member(X1987,X1983,X1984)
| ~ c_Fun_Oinj__on(X1987,X1986,X1985,X1984) )
& ( X1983 != X1982
| hAPP(X1985,X1983) = hAPP(X1985,X1982)
| ~ c_member(X1987,X1982,X1984)
| ~ c_member(X1987,X1983,X1984)
| ~ c_Fun_Oinj__on(X1987,X1986,X1985,X1984) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).
fof(i_0_667,plain,
! [X1988,X1989,X1990,X1991,X1992,X1993] :
( ~ c_Fun_Oinj__on(X1993,X1992,X1991,X1990)
| hAPP(X1991,X1989) != hAPP(X1991,X1988)
| ~ c_member(X1993,X1989,X1990)
| ~ c_member(X1993,X1988,X1990)
| X1989 = X1988 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).
fof(i_0_668,plain,
! [X1976,X1977,X1978,X1979,X1980,X1981] :
( ~ c_Fun_Oinj__on(X1981,X1980,X1979,X1978)
| X1977 = X1976
| ~ c_member(X1981,X1977,X1978)
| ~ c_member(X1981,X1976,X1978)
| hAPP(X1979,X1977) != hAPP(X1979,X1976) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).
fof(i_0_669,plain,
! [X2934,X2935,X2936,X2937,X2938] :
( ( c_Orderings_Oord__class_Oless__eq(X2938,X2935,X2937)
| ~ c_Orderings_Oord__class_Oless__eq(X2938,X2937,X2936)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2938,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2938,X2937,X2936),c_SetInterval_Oord__class_OatLeastAtMost(X2938,X2935,X2934))
| ~ class_Orderings_Oorder(X2938) )
& ( c_Orderings_Oord__class_Oless__eq(X2938,X2936,X2934)
| ~ c_Orderings_Oord__class_Oless__eq(X2938,X2937,X2936)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2938,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2938,X2937,X2936),c_SetInterval_Oord__class_OatLeastAtMost(X2938,X2935,X2934))
| ~ class_Orderings_Oorder(X2938) )
& ( c_Orderings_Oord__class_Oless__eq(X2938,X2937,X2936)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2938,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2938,X2937,X2936),c_SetInterval_Oord__class_OatLeastAtMost(X2938,X2935,X2934))
| ~ class_Orderings_Oorder(X2938) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2938,X2935,X2937)
| ~ c_Orderings_Oord__class_Oless__eq(X2938,X2936,X2934)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2938,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(X2938,X2937,X2936),c_SetInterval_Oord__class_OatLeastAtMost(X2938,X2935,X2934))
| ~ class_Orderings_Oorder(X2938) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])])]) ).
fof(i_0_670,plain,
! [X3074,X3075,X3076] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3076,tc_HOL_Obool),X3075,c_Set_Oinsert(X3076,X3074,c_Orderings_Obot__class_Obot(tc_fun(X3076,tc_HOL_Obool))))
| X3075 = c_Orderings_Obot__class_Obot(tc_fun(X3076,tc_HOL_Obool))
| X3075 = c_Set_Oinsert(X3076,X3074,c_Orderings_Obot__class_Obot(tc_fun(X3076,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__singletonD])]) ).
fof(i_0_671,plain,
! [X2519,X2520,X2521,X2522] :
( ~ c_Finite__Set_Ofinite(X2522,X2521)
| ~ c_Finite__Set_Ofinite(X2520,X2519)
| c_Finite__Set_Ofinite(tc_sum(X2522,X2520),c_Sum__Type_OPlus(X2522,X2520,X2521,X2519)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).
fof(i_0_672,plain,
! [X2317,X2318,X2319,X2320,X2321] :
( ( c_Orderings_Oord__class_Oless__eq(X2321,X2318,X2320)
| c_Orderings_Oord__class_Oless__eq(X2321,X2319,X2320)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2321,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X2321,X2320,X2319),c_SetInterval_Oord__class_OatLeastLessThan(X2321,X2318,X2317))
| ~ class_Orderings_Olinorder(X2321) )
& ( c_Orderings_Oord__class_Oless__eq(X2321,X2319,X2317)
| c_Orderings_Oord__class_Oless__eq(X2321,X2319,X2320)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2321,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X2321,X2320,X2319),c_SetInterval_Oord__class_OatLeastLessThan(X2321,X2318,X2317))
| ~ class_Orderings_Olinorder(X2321) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).
fof(i_0_673,plain,
! [X2827,X2828,X2829,X2830,X2831] :
( ~ class_Rings_Ocomm__semiring__1(X2831)
| c_Groups_Oplus__class_Oplus(X2831,c_Groups_Oplus__class_Oplus(X2831,X2830,X2829),c_Groups_Oplus__class_Oplus(X2831,X2828,X2827)) = c_Groups_Oplus__class_Oplus(X2831,c_Groups_Oplus__class_Oplus(X2831,X2830,X2828),c_Groups_Oplus__class_Oplus(X2831,X2829,X2827)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_674,plain,
! [X2529,X2530,X2531,X2532] :
( ( X2530 = c_Orderings_Obot__class_Obot(tc_fun(X2532,tc_HOL_Obool))
| c_Sum__Type_OPlus(X2532,X2531,X2530,X2529) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2532,X2531),tc_HOL_Obool)) )
& ( X2529 = c_Orderings_Obot__class_Obot(tc_fun(X2531,tc_HOL_Obool))
| c_Sum__Type_OPlus(X2532,X2531,X2530,X2529) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2532,X2531),tc_HOL_Obool)) )
& ( X2530 != c_Orderings_Obot__class_Obot(tc_fun(X2532,tc_HOL_Obool))
| X2529 != c_Orderings_Obot__class_Obot(tc_fun(X2531,tc_HOL_Obool))
| c_Sum__Type_OPlus(X2532,X2531,X2530,X2529) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2532,X2531),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_675,plain,
! [X1643,X1644,X1645,X1646] :
( ~ c_Finite__Set_Ofinite(X1646,X1645)
| c_Finite__Set_Ofinite(X1644,c_Set_Oimage(X1646,X1644,X1643,X1645)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
fof(i_0_676,plain,
! [X1616,X1617,X1618,X1619,X1620] :
( ( hAPP(X1618,X1617) != hAPP(X1618,X1616)
| X1617 = X1616
| ~ c_Fun_Oinj__on(X1620,X1619,X1618,c_Orderings_Otop__class_Otop(tc_fun(X1620,tc_HOL_Obool))) )
& ( X1617 != X1616
| hAPP(X1618,X1617) = hAPP(X1618,X1616)
| ~ c_Fun_Oinj__on(X1620,X1619,X1618,c_Orderings_Otop__class_Otop(tc_fun(X1620,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).
fof(i_0_677,plain,
! [X1621,X1622,X1623,X1624,X1625] :
( ~ c_Fun_Oinj__on(X1625,X1624,X1623,c_Orderings_Otop__class_Otop(tc_fun(X1625,tc_HOL_Obool)))
| hAPP(X1623,X1622) != hAPP(X1623,X1621)
| X1622 = X1621 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).
fof(i_0_678,plain,
! [X2879,X2880,X2881,X2882] :
( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2881,tc_Nat_Onat,X2879,X2880) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_member(X2881,X2882,X2880)
| hAPP(X2879,X2882) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2881,X2880) )
& ( c_member(X2881,esk28_3(X2879,X2880,X2881),X2880)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2881,tc_Nat_Onat,X2879,X2880) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2881,X2880) )
& ( hAPP(X2879,esk28_3(X2879,X2880,X2881)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2881,tc_Nat_Onat,X2879,X2880) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2881,X2880) ) ),
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_679,plain,
! [X2682,X2683,X2684,X2685] :
( ( ~ c_Orderings_Oord__class_Oless(X2685,c_Groups_Oplus__class_Oplus(X2685,X2684,X2683),c_Groups_Oplus__class_Oplus(X2685,X2682,X2683))
| c_Orderings_Oord__class_Oless(X2685,X2684,X2682)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2685) )
& ( ~ c_Orderings_Oord__class_Oless(X2685,X2684,X2682)
| c_Orderings_Oord__class_Oless(X2685,c_Groups_Oplus__class_Oplus(X2685,X2684,X2683),c_Groups_Oplus__class_Oplus(X2685,X2682,X2683))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2685) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_680,plain,
! [X2661,X2662,X2663,X2664] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2664)
| ~ c_Orderings_Oord__class_Oless(X2664,c_Groups_Oplus__class_Oplus(X2664,X2663,X2662),c_Groups_Oplus__class_Oplus(X2664,X2661,X2662))
| c_Orderings_Oord__class_Oless(X2664,X2663,X2661) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_681,plain,
! [X2678,X2679,X2680,X2681] :
( ( ~ c_Orderings_Oord__class_Oless(X2681,c_Groups_Oplus__class_Oplus(X2681,X2680,X2679),c_Groups_Oplus__class_Oplus(X2681,X2680,X2678))
| c_Orderings_Oord__class_Oless(X2681,X2679,X2678)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2681) )
& ( ~ c_Orderings_Oord__class_Oless(X2681,X2679,X2678)
| c_Orderings_Oord__class_Oless(X2681,c_Groups_Oplus__class_Oplus(X2681,X2680,X2679),c_Groups_Oplus__class_Oplus(X2681,X2680,X2678))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2681) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_682,plain,
! [X2657,X2658,X2659,X2660] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2660)
| ~ c_Orderings_Oord__class_Oless(X2660,c_Groups_Oplus__class_Oplus(X2660,X2659,X2658),c_Groups_Oplus__class_Oplus(X2660,X2659,X2657))
| c_Orderings_Oord__class_Oless(X2660,X2658,X2657) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_683,plain,
! [X2721,X2722,X2723,X2724] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2724,c_Groups_Oplus__class_Oplus(X2724,X2723,X2722),c_Groups_Oplus__class_Oplus(X2724,X2721,X2722))
| c_Orderings_Oord__class_Oless__eq(X2724,X2723,X2721)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2724) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2724,X2723,X2721)
| c_Orderings_Oord__class_Oless__eq(X2724,c_Groups_Oplus__class_Oplus(X2724,X2723,X2722),c_Groups_Oplus__class_Oplus(X2724,X2721,X2722))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2724) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_684,plain,
! [X2700,X2701,X2702,X2703] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2703)
| ~ c_Orderings_Oord__class_Oless__eq(X2703,c_Groups_Oplus__class_Oplus(X2703,X2702,X2701),c_Groups_Oplus__class_Oplus(X2703,X2700,X2701))
| c_Orderings_Oord__class_Oless__eq(X2703,X2702,X2700) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_685,plain,
! [X2717,X2718,X2719,X2720] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2720,c_Groups_Oplus__class_Oplus(X2720,X2719,X2718),c_Groups_Oplus__class_Oplus(X2720,X2719,X2717))
| c_Orderings_Oord__class_Oless__eq(X2720,X2718,X2717)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2720) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2720,X2718,X2717)
| c_Orderings_Oord__class_Oless__eq(X2720,c_Groups_Oplus__class_Oplus(X2720,X2719,X2718),c_Groups_Oplus__class_Oplus(X2720,X2719,X2717))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2720) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_686,plain,
! [X2696,X2697,X2698,X2699] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2699)
| ~ c_Orderings_Oord__class_Oless__eq(X2699,c_Groups_Oplus__class_Oplus(X2699,X2698,X2697),c_Groups_Oplus__class_Oplus(X2699,X2698,X2696))
| c_Orderings_Oord__class_Oless__eq(X2699,X2697,X2696) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_687,plain,
! [X3168,X3169,X3170,X3173,X3174,X3175,X3176,X3177] :
( ( X3169 = c_Set_Oinsert(X3170,esk43_3(X3168,X3169,X3170),esk44_3(X3168,X3169,X3170))
| c_Finite__Set_Ocard(X3170,X3169) != hAPP(c_Nat_OSuc,X3168) )
& ( ~ c_member(X3170,esk43_3(X3168,X3169,X3170),esk44_3(X3168,X3169,X3170))
| c_Finite__Set_Ocard(X3170,X3169) != hAPP(c_Nat_OSuc,X3168) )
& ( c_Finite__Set_Ocard(X3170,esk44_3(X3168,X3169,X3170)) = X3168
| c_Finite__Set_Ocard(X3170,X3169) != hAPP(c_Nat_OSuc,X3168) )
& ( X3168 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| esk44_3(X3168,X3169,X3170) = c_Orderings_Obot__class_Obot(tc_fun(X3170,tc_HOL_Obool))
| c_Finite__Set_Ocard(X3170,X3169) != hAPP(c_Nat_OSuc,X3168) )
& ( X3173 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3174 != c_Set_Oinsert(X3175,X3176,X3177)
| c_member(X3175,X3176,X3177)
| c_Finite__Set_Ocard(X3175,X3177) != X3173
| c_Finite__Set_Ocard(X3175,X3174) = hAPP(c_Nat_OSuc,X3173) )
& ( X3177 != c_Orderings_Obot__class_Obot(tc_fun(X3175,tc_HOL_Obool))
| X3174 != c_Set_Oinsert(X3175,X3176,X3177)
| c_member(X3175,X3176,X3177)
| c_Finite__Set_Ocard(X3175,X3177) != X3173
| c_Finite__Set_Ocard(X3175,X3174) = hAPP(c_Nat_OSuc,X3173) ) ),
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_526])])])])])]) ).
fof(i_0_688,plain,
! [X2628,X2629,X2630] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2630,X2629),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2630,X2628))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2629,X2628) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2629,X2628)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2630,X2629),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2630,X2628)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_689,plain,
! [X2599,X2600,X2601] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2601,X2600),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2601,X2599))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2600,X2599) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2600,X2599)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2601,X2600),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2601,X2599)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_690,plain,
! [X2242,X2243,X2244,X2245] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2245,tc_HOL_Obool)) != c_Set_Oimage(X2244,X2245,X2243,X2242)
| X2242 = c_Orderings_Obot__class_Obot(tc_fun(X2244,tc_HOL_Obool)) )
& ( X2242 != c_Orderings_Obot__class_Obot(tc_fun(X2244,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X2245,tc_HOL_Obool)) = c_Set_Oimage(X2244,X2245,X2243,X2242) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])]) ).
fof(i_0_691,plain,
! [X2235,X2236,X2237,X2238] :
( ( c_Set_Oimage(X2238,X2237,X2236,X2235) != c_Orderings_Obot__class_Obot(tc_fun(X2237,tc_HOL_Obool))
| X2235 = c_Orderings_Obot__class_Obot(tc_fun(X2238,tc_HOL_Obool)) )
& ( X2235 != c_Orderings_Obot__class_Obot(tc_fun(X2238,tc_HOL_Obool))
| c_Set_Oimage(X2238,X2237,X2236,X2235) = c_Orderings_Obot__class_Obot(tc_fun(X2237,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])]) ).
fof(i_0_692,plain,
! [X2376,X2377] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2377,X2376),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2377,X2376),tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2376,c_Orderings_Otop__class_Otop(tc_fun(X2376,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Finite__Set_Ofinite(X2377,c_Orderings_Otop__class_Otop(tc_fun(X2377,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).
fof(i_0_693,plain,
! [X2665,X2666,X2667,X2668,X2669] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2669)
| ~ c_Orderings_Oord__class_Oless(X2669,X2668,X2667)
| ~ c_Orderings_Oord__class_Oless(X2669,X2666,X2665)
| c_Orderings_Oord__class_Oless(X2669,c_Groups_Oplus__class_Oplus(X2669,X2668,X2666),c_Groups_Oplus__class_Oplus(X2669,X2667,X2665)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_694,plain,
! [X2757,X2758,X2759,X2760,X2761] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2761)
| ~ c_Orderings_Oord__class_Oless__eq(X2761,X2760,X2759)
| ~ c_Orderings_Oord__class_Oless(X2761,X2758,X2757)
| c_Orderings_Oord__class_Oless(X2761,c_Groups_Oplus__class_Oplus(X2761,X2760,X2758),c_Groups_Oplus__class_Oplus(X2761,X2759,X2757)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_695,plain,
! [X2752,X2753,X2754,X2755,X2756] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2756)
| ~ c_Orderings_Oord__class_Oless(X2756,X2755,X2754)
| ~ c_Orderings_Oord__class_Oless__eq(X2756,X2753,X2752)
| c_Orderings_Oord__class_Oless(X2756,c_Groups_Oplus__class_Oplus(X2756,X2755,X2753),c_Groups_Oplus__class_Oplus(X2756,X2754,X2752)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_696,plain,
! [X2704,X2705,X2706,X2707,X2708] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2708)
| ~ c_Orderings_Oord__class_Oless__eq(X2708,X2707,X2706)
| ~ c_Orderings_Oord__class_Oless__eq(X2708,X2705,X2704)
| c_Orderings_Oord__class_Oless__eq(X2708,c_Groups_Oplus__class_Oplus(X2708,X2707,X2705),c_Groups_Oplus__class_Oplus(X2708,X2706,X2704)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_697,plain,
! [X2966,X2967] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2967,X2966)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2967),hAPP(c_Nat_OSuc,X2966)),
inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastAtMost]) ).
fof(i_0_698,plain,
! [X2421,X2422] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2422,X2421)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2422),hAPP(c_Nat_OSuc,X2421)),
inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).
fof(i_0_699,plain,
! [X3006,X3007,X3009] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk41_2(X3006,X3007),X3006)
| ~ hBOOL(hAPP(X3007,X3006))
| hBOOL(hAPP(X3007,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3009,esk41_2(X3006,X3007))
| ~ hBOOL(hAPP(X3007,X3009))
| ~ hBOOL(hAPP(X3007,X3006))
| hBOOL(hAPP(X3007,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X3007,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk41_2(X3006,X3007),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X3007,X3006))
| hBOOL(hAPP(X3007,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_527])])])])]) ).
fof(i_0_700,plain,
! [X2527,X2528] : c_Sum__Type_OPlus(X2528,X2527,c_Orderings_Otop__class_Otop(tc_fun(X2528,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2527,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2528,X2527),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(i_0_701,plain,
! [X2640,X2641,X2642,X2643] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2643,X2642)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2641,X2640)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2643,X2641),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2642,X2640)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_702,plain,
! [X2611,X2612,X2613,X2614] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2614,X2613)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2612,X2611)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2614,X2612),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2613,X2611)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_703,plain,
! [X3065,X3066,X3067,X3068] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3068,tc_HOL_Obool),X3066,c_Set_Oinsert(X3068,X3067,X3065))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3068,tc_HOL_Obool),X3066,X3065)
| c_member(X3068,X3067,X3066) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3068,tc_HOL_Obool),X3066,X3065)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3068,tc_HOL_Obool),X3066,c_Set_Oinsert(X3068,X3067,X3065))
| c_member(X3068,X3067,X3066) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])])]) ).
fof(i_0_704,plain,
! [X3058,X3059,X3060] :
( ~ c_member(X3060,X3059,c_Set_Oinsert(X3060,X3058,c_Orderings_Obot__class_Obot(tc_fun(X3060,tc_HOL_Obool))))
| X3059 = X3058 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singletonE])]) ).
fof(i_0_705,plain,
! [X3055,X3056,X3057] :
( ( ~ c_member(X3057,X3056,c_Set_Oinsert(X3057,X3055,c_Orderings_Obot__class_Obot(tc_fun(X3057,tc_HOL_Obool))))
| X3056 = X3055 )
& ( X3056 != X3055
| c_member(X3057,X3056,c_Set_Oinsert(X3057,X3055,c_Orderings_Obot__class_Obot(tc_fun(X3057,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__iff])]) ).
fof(i_0_706,plain,
! [X2958,X2959,X2961,X2962,X2963,X2965] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk37_2(X2958,X2959),X2959)
| ~ c_member(tc_Nat_Onat,X2961,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2959))
| hBOOL(hAPP(X2958,X2961)) )
& ( ~ hBOOL(hAPP(X2958,esk37_2(X2958,X2959)))
| ~ c_member(tc_Nat_Onat,X2961,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2959))
| hBOOL(hAPP(X2958,X2961)) )
& ( c_member(tc_Nat_Onat,esk38_2(X2962,X2963),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2963))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2965,X2963)
| hBOOL(hAPP(X2962,X2965)) )
& ( ~ hBOOL(hAPP(X2962,esk38_2(X2962,X2963)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2965,X2963)
| hBOOL(hAPP(X2962,X2965)) ) ),
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_707,plain,
! [X2322,X2323,X2325,X2326,X2327,X2329] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk20_2(X2322,X2323),X2323)
| ~ c_member(tc_Nat_Onat,X2325,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2323))
| hBOOL(hAPP(X2322,X2325)) )
& ( ~ hBOOL(hAPP(X2322,esk20_2(X2322,X2323)))
| ~ c_member(tc_Nat_Onat,X2325,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2323))
| hBOOL(hAPP(X2322,X2325)) )
& ( c_member(tc_Nat_Onat,esk21_2(X2326,X2327),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2327))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2329,X2327)
| hBOOL(hAPP(X2326,X2329)) )
& ( ~ hBOOL(hAPP(X2326,esk21_2(X2326,X2327)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2329,X2327)
| hBOOL(hAPP(X2326,X2329)) ) ),
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_708,plain,
! [X3089,X3090,X3091,X3092] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X3092,X3091,X3090),X3089))
| X3091 = X3089
| hBOOL(hAPP(X3090,X3089)) )
& ( X3091 != X3089
| hBOOL(hAPP(c_Set_Oinsert(X3092,X3091,X3090),X3089)) )
& ( ~ hBOOL(hAPP(X3090,X3089))
| hBOOL(hAPP(c_Set_Oinsert(X3092,X3091,X3090),X3089)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(i_0_709,plain,
! [X3044,X3045,X3046,X3047] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3047,tc_HOL_Obool),X3046,X3045)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3047,tc_HOL_Obool),c_Set_Oinsert(X3047,X3044,X3046),c_Set_Oinsert(X3047,X3044,X3045)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
fof(i_0_710,plain,
! [X1656,X1657] :
( ~ c_Finite__Set_Ofinite(X1657,c_Orderings_Otop__class_Otop(tc_fun(X1657,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X1656,c_Orderings_Otop__class_Otop(tc_fun(X1656,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_prod(X1657,X1656),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1657,X1656),tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).
fof(i_0_711,plain,
! [X1650,X1651] :
( ( c_Finite__Set_Ofinite(X1651,c_Orderings_Otop__class_Otop(tc_fun(X1651,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X1651,X1650),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1651,X1650),tc_HOL_Obool))) )
& ( c_Finite__Set_Ofinite(X1650,c_Orderings_Otop__class_Otop(tc_fun(X1650,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X1651,X1650),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1651,X1650),tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X1651,c_Orderings_Otop__class_Otop(tc_fun(X1651,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X1650,c_Orderings_Otop__class_Otop(tc_fun(X1650,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_sum(X1651,X1650),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1651,X1650),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_712,plain,
! [X3061,X3062,X3063,X3064] :
( ( c_member(X3064,X3063,X3061)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3064,tc_HOL_Obool),c_Set_Oinsert(X3064,X3063,X3062),X3061) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3064,tc_HOL_Obool),X3062,X3061)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3064,tc_HOL_Obool),c_Set_Oinsert(X3064,X3063,X3062),X3061) )
& ( ~ c_member(X3064,X3063,X3061)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3064,tc_HOL_Obool),X3062,X3061)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3064,tc_HOL_Obool),c_Set_Oinsert(X3064,X3063,X3062),X3061) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).
fof(i_0_713,plain,
! [X2378,X2379,X2380,X2381,X2382] :
( ~ c_Finite__Set_Ofolding__one__idem(X2382,X2381,X2380)
| ~ c_Finite__Set_Ofinite(X2382,X2379)
| X2378 = c_Orderings_Obot__class_Obot(tc_fun(X2382,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2382,tc_HOL_Obool),X2378,X2379)
| hAPP(hAPP(X2381,hAPP(X2380,X2378)),hAPP(X2380,X2379)) = hAPP(X2380,X2379) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem])]) ).
fof(i_0_714,plain,
! [X2177,X2178,X2179] :
( ~ c_Finite__Set_Ofinite(X2179,X2178)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2179,tc_HOL_Obool),X2177,X2178)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(X2179,X2177),c_Finite__Set_Ocard(X2179,X2178))
| c_Orderings_Oord__class_Oless(tc_fun(X2179,tc_HOL_Obool),X2177,X2178) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).
fof(i_0_715,plain,
! [X2950,X2951,X2952,X2954,X2955,X2956] :
( ( c_member(tc_Nat_Onat,esk35_2(X2950,X2951),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2951))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2952,X2951)
| ~ hBOOL(hAPP(X2950,X2952)) )
& ( hBOOL(hAPP(X2950,esk35_2(X2950,X2951)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2952,X2951)
| ~ hBOOL(hAPP(X2950,X2952)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk36_2(X2954,X2955),X2955)
| ~ c_member(tc_Nat_Onat,X2956,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2955))
| ~ hBOOL(hAPP(X2954,X2956)) )
& ( hBOOL(hAPP(X2954,esk36_2(X2954,X2955)))
| ~ c_member(tc_Nat_Onat,X2956,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2955))
| ~ hBOOL(hAPP(X2954,X2956)) ) ),
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_716,plain,
! [X2057,X2058,X2059,X2061,X2062,X2063] :
( ( c_member(tc_Nat_Onat,esk10_2(X2057,X2058),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2058))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2059,X2058)
| ~ hBOOL(hAPP(X2057,X2059)) )
& ( hBOOL(hAPP(X2057,esk10_2(X2057,X2058)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2059,X2058)
| ~ hBOOL(hAPP(X2057,X2059)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk11_2(X2061,X2062),X2062)
| ~ c_member(tc_Nat_Onat,X2063,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2062))
| ~ hBOOL(hAPP(X2061,X2063)) )
& ( hBOOL(hAPP(X2061,esk11_2(X2061,X2062)))
| ~ c_member(tc_Nat_Onat,X2063,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2062))
| ~ hBOOL(hAPP(X2061,X2063)) ) ),
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_717,plain,
! [X3017,X3018] :
( ~ class_Int_Oring__char__0(X3018)
| ~ c_member(X3018,X3017,c_Int_Oring__1__class_OInts(X3018))
| c_Groups_Oplus__class_Oplus(X3018,c_Groups_Oplus__class_Oplus(X3018,c_Groups_Oone__class_Oone(X3018),X3017),X3017) != c_Groups_Ozero__class_Ozero(X3018) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).
fof(i_0_718,plain,
! [X3178,X3179,X3180,X3181,X3182] :
( ~ c_Finite__Set_Ofolding__one(X3182,X3181,X3180)
| ~ c_Finite__Set_Ofinite(X3182,X3179)
| c_member(X3182,X3178,X3179)
| X3179 = c_Orderings_Obot__class_Obot(tc_fun(X3182,tc_HOL_Obool))
| hAPP(X3180,c_Set_Oinsert(X3182,X3178,X3179)) = hAPP(hAPP(X3181,X3178),hAPP(X3180,X3179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])]) ).
fof(i_0_719,plain,
! [X3140,X3141] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3141,hAPP(c_Nat_OSuc,X3140))
| c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3141,hAPP(c_Nat_OSuc,X3140)) = c_Set_Oinsert(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3140),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3141,X3140)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv])]) ).
fof(i_0_720,plain,
! [X1654,X1655] :
( ~ c_Finite__Set_Ofinite(tc_fun(X1655,X1654),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1655,X1654),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X1654,c_Orderings_Otop__class_Otop(tc_fun(X1654,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).
fof(i_0_721,plain,
! [X2762,X2763,X2764] :
( ~ class_Groups_Oordered__comm__monoid__add(X2764)
| ~ c_Orderings_Oord__class_Oless(X2764,X2763,c_Groups_Ozero__class_Ozero(X2764))
| ~ c_Orderings_Oord__class_Oless(X2764,X2762,c_Groups_Ozero__class_Ozero(X2764))
| c_Orderings_Oord__class_Oless(X2764,c_Groups_Oplus__class_Oplus(X2764,X2763,X2762),c_Groups_Ozero__class_Ozero(X2764)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_722,plain,
! [X2805,X2806,X2807] :
( ~ class_Groups_Oordered__comm__monoid__add(X2807)
| ~ c_Orderings_Oord__class_Oless__eq(X2807,X2806,c_Groups_Ozero__class_Ozero(X2807))
| ~ c_Orderings_Oord__class_Oless(X2807,X2805,c_Groups_Ozero__class_Ozero(X2807))
| c_Orderings_Oord__class_Oless(X2807,c_Groups_Oplus__class_Oplus(X2807,X2806,X2805),c_Groups_Ozero__class_Ozero(X2807)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_723,plain,
! [X2802,X2803,X2804] :
( ~ class_Groups_Oordered__comm__monoid__add(X2804)
| ~ c_Orderings_Oord__class_Oless(X2804,X2803,c_Groups_Ozero__class_Ozero(X2804))
| ~ c_Orderings_Oord__class_Oless__eq(X2804,X2802,c_Groups_Ozero__class_Ozero(X2804))
| c_Orderings_Oord__class_Oless(X2804,c_Groups_Oplus__class_Oplus(X2804,X2803,X2802),c_Groups_Ozero__class_Ozero(X2804)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_724,plain,
! [X2731,X2732,X2733] :
( ~ class_Groups_Oordered__comm__monoid__add(X2733)
| ~ c_Orderings_Oord__class_Oless__eq(X2733,X2732,c_Groups_Ozero__class_Ozero(X2733))
| ~ c_Orderings_Oord__class_Oless__eq(X2733,X2731,c_Groups_Ozero__class_Ozero(X2733))
| c_Orderings_Oord__class_Oless__eq(X2733,c_Groups_Oplus__class_Oplus(X2733,X2732,X2731),c_Groups_Ozero__class_Ozero(X2733)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_725,plain,
! [X3011,X3012,X3013] :
( ~ class_Rings_Oring__1(X3013)
| ~ c_member(X3013,X3012,c_Int_Oring__1__class_OInts(X3013))
| ~ c_member(X3013,X3011,c_Int_Oring__1__class_OInts(X3013))
| c_member(X3013,c_Groups_Oplus__class_Oplus(X3013,X3012,X3011),c_Int_Oring__1__class_OInts(X3013)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).
fof(i_0_726,plain,
! [X2765,X2766,X2767] :
( ~ class_Groups_Oordered__comm__monoid__add(X2767)
| ~ c_Orderings_Oord__class_Oless(X2767,c_Groups_Ozero__class_Ozero(X2767),X2766)
| ~ c_Orderings_Oord__class_Oless(X2767,c_Groups_Ozero__class_Ozero(X2767),X2765)
| c_Orderings_Oord__class_Oless(X2767,c_Groups_Ozero__class_Ozero(X2767),c_Groups_Oplus__class_Oplus(X2767,X2766,X2765)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_727,plain,
! [X2791,X2792,X2793] :
( ~ class_Groups_Oordered__comm__monoid__add(X2793)
| ~ c_Orderings_Oord__class_Oless__eq(X2793,c_Groups_Ozero__class_Ozero(X2793),X2792)
| ~ c_Orderings_Oord__class_Oless(X2793,c_Groups_Ozero__class_Ozero(X2793),X2791)
| c_Orderings_Oord__class_Oless(X2793,c_Groups_Ozero__class_Ozero(X2793),c_Groups_Oplus__class_Oplus(X2793,X2792,X2791)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_728,plain,
! [X2788,X2789,X2790] :
( ~ class_Groups_Oordered__comm__monoid__add(X2790)
| ~ c_Orderings_Oord__class_Oless(X2790,c_Groups_Ozero__class_Ozero(X2790),X2789)
| ~ c_Orderings_Oord__class_Oless__eq(X2790,c_Groups_Ozero__class_Ozero(X2790),X2788)
| c_Orderings_Oord__class_Oless(X2790,c_Groups_Ozero__class_Ozero(X2790),c_Groups_Oplus__class_Oplus(X2790,X2789,X2788)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_729,plain,
! [X2745,X2746,X2747] :
( ~ class_Groups_Oordered__comm__monoid__add(X2747)
| ~ c_Orderings_Oord__class_Oless__eq(X2747,c_Groups_Ozero__class_Ozero(X2747),X2746)
| ~ c_Orderings_Oord__class_Oless__eq(X2747,c_Groups_Ozero__class_Ozero(X2747),X2745)
| c_Orderings_Oord__class_Oless__eq(X2747,c_Groups_Ozero__class_Ozero(X2747),c_Groups_Oplus__class_Oplus(X2747,X2746,X2745)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_730,plain,
! [X2776,X2777] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2777,X2776))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2777)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2776) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2777)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2777,X2776)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2776)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2777,X2776)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_731,plain,
! [X2674,X2675,X2676,X2677] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2677)
| ~ c_Orderings_Oord__class_Oless(X2677,X2676,X2675)
| c_Orderings_Oord__class_Oless(X2677,c_Groups_Oplus__class_Oplus(X2677,X2676,X2674),c_Groups_Oplus__class_Oplus(X2677,X2675,X2674)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_732,plain,
! [X2670,X2671,X2672,X2673] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2673)
| ~ c_Orderings_Oord__class_Oless(X2673,X2672,X2671)
| c_Orderings_Oord__class_Oless(X2673,c_Groups_Oplus__class_Oplus(X2673,X2670,X2672),c_Groups_Oplus__class_Oplus(X2673,X2670,X2671)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_733,plain,
! [X2713,X2714,X2715,X2716] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2716)
| ~ c_Orderings_Oord__class_Oless__eq(X2716,X2715,X2714)
| c_Orderings_Oord__class_Oless__eq(X2716,c_Groups_Oplus__class_Oplus(X2716,X2715,X2713),c_Groups_Oplus__class_Oplus(X2716,X2714,X2713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_734,plain,
! [X2709,X2710,X2711,X2712] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2712)
| ~ c_Orderings_Oord__class_Oless__eq(X2712,X2711,X2710)
| c_Orderings_Oord__class_Oless__eq(X2712,c_Groups_Oplus__class_Oplus(X2712,X2709,X2711),c_Groups_Oplus__class_Oplus(X2712,X2709,X2710)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_735,plain,
! [X2293,X2294,X2295,X2296,X2297] :
( ( X2296 = X2294
| c_SetInterval_Oord__class_OatLeastLessThan(X2297,X2296,X2295) != c_SetInterval_Oord__class_OatLeastLessThan(X2297,X2294,X2293)
| ~ c_Orderings_Oord__class_Oless(X2297,X2294,X2293)
| ~ c_Orderings_Oord__class_Oless(X2297,X2296,X2295)
| ~ class_Orderings_Olinorder(X2297) )
& ( X2295 = X2293
| c_SetInterval_Oord__class_OatLeastLessThan(X2297,X2296,X2295) != c_SetInterval_Oord__class_OatLeastLessThan(X2297,X2294,X2293)
| ~ c_Orderings_Oord__class_Oless(X2297,X2294,X2293)
| ~ c_Orderings_Oord__class_Oless(X2297,X2296,X2295)
| ~ class_Orderings_Olinorder(X2297) )
& ( X2296 != X2294
| X2295 != X2293
| c_SetInterval_Oord__class_OatLeastLessThan(X2297,X2296,X2295) = c_SetInterval_Oord__class_OatLeastLessThan(X2297,X2294,X2293)
| ~ c_Orderings_Oord__class_Oless(X2297,X2294,X2293)
| ~ c_Orderings_Oord__class_Oless(X2297,X2296,X2295)
| ~ class_Orderings_Olinorder(X2297) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).
fof(i_0_736,plain,
! [X2288,X2289,X2290,X2291,X2292] :
( ~ class_Orderings_Olinorder(X2292)
| c_SetInterval_Oord__class_OatLeastLessThan(X2292,X2291,X2290) != c_SetInterval_Oord__class_OatLeastLessThan(X2292,X2289,X2288)
| ~ c_Orderings_Oord__class_Oless(X2292,X2291,X2290)
| ~ c_Orderings_Oord__class_Oless(X2292,X2289,X2288)
| X2291 = X2289 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).
fof(i_0_737,plain,
! [X2283,X2284,X2285,X2286,X2287] :
( ~ class_Orderings_Olinorder(X2287)
| c_SetInterval_Oord__class_OatLeastLessThan(X2287,X2286,X2285) != c_SetInterval_Oord__class_OatLeastLessThan(X2287,X2284,X2283)
| ~ c_Orderings_Oord__class_Oless(X2287,X2286,X2285)
| ~ c_Orderings_Oord__class_Oless(X2287,X2284,X2283)
| X2285 = X2283 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).
fof(i_0_738,plain,
! [X2812,X2813,X2814,X2815] :
( ~ class_Rings_Olinordered__semidom(X2815)
| ~ c_Orderings_Oord__class_Oless(X2815,c_Groups_Ozero__class_Ozero(X2815),X2814)
| ~ c_Orderings_Oord__class_Oless(X2815,X2813,X2812)
| c_Orderings_Oord__class_Oless(X2815,X2813,c_Groups_Oplus__class_Oplus(X2815,X2814,X2812)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_739,plain,
! [X2798,X2799,X2800,X2801] :
( ~ class_Groups_Oordered__comm__monoid__add(X2801)
| ~ c_Orderings_Oord__class_Oless__eq(X2801,c_Groups_Ozero__class_Ozero(X2801),X2800)
| ~ c_Orderings_Oord__class_Oless(X2801,X2799,X2798)
| c_Orderings_Oord__class_Oless(X2801,X2799,c_Groups_Oplus__class_Oplus(X2801,X2800,X2798)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_740,plain,
! [X2794,X2795,X2796,X2797] :
( ~ class_Groups_Oordered__comm__monoid__add(X2797)
| ~ c_Orderings_Oord__class_Oless(X2797,c_Groups_Ozero__class_Ozero(X2797),X2796)
| ~ c_Orderings_Oord__class_Oless__eq(X2797,X2795,X2794)
| c_Orderings_Oord__class_Oless(X2797,X2795,c_Groups_Oplus__class_Oplus(X2797,X2796,X2794)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_741,plain,
! [X2738,X2739,X2740,X2741] :
( ~ class_Groups_Oordered__comm__monoid__add(X2741)
| ~ c_Orderings_Oord__class_Oless__eq(X2741,c_Groups_Ozero__class_Ozero(X2741),X2740)
| ~ c_Orderings_Oord__class_Oless__eq(X2741,X2739,X2738)
| c_Orderings_Oord__class_Oless__eq(X2741,X2739,c_Groups_Oplus__class_Oplus(X2741,X2740,X2738)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_742,plain,
! [X2734,X2735,X2736,X2737] :
( ~ class_Groups_Oordered__comm__monoid__add(X2737)
| ~ c_Orderings_Oord__class_Oless__eq(X2737,c_Groups_Ozero__class_Ozero(X2737),X2736)
| ~ c_Orderings_Oord__class_Oless__eq(X2737,X2735,X2734)
| c_Orderings_Oord__class_Oless__eq(X2737,X2735,c_Groups_Oplus__class_Oplus(X2737,X2734,X2736)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_743,plain,
! [X2637,X2638,X2639] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2639,X2638)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2639,X2637),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2638,X2637)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_744,plain,
! [X2608,X2609,X2610] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2610,X2609)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2610,X2608),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2609,X2608)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_745,plain,
! [X3137,X3138,X3139] :
( ~ c_Finite__Set_Ofinite(X3139,X3138)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3139,X3138),c_Finite__Set_Ocard(X3139,c_Set_Oinsert(X3139,X3137,X3138))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).
fof(i_0_746,plain,
! [X3114,X3115,X3116] :
( c_Set_Oinsert(X3116,X3115,c_Orderings_Obot__class_Obot(tc_fun(X3116,tc_HOL_Obool))) != c_Set_Oinsert(X3116,X3114,c_Orderings_Obot__class_Obot(tc_fun(X3116,tc_HOL_Obool)))
| X3115 = X3114 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])]) ).
fof(i_0_747,plain,
! [X2338,X2339,X2340,X2341] :
( ( ~ c_member(X2341,X2340,c_SetInterval_Oord_OlessThan(X2341,X2339,X2338))
| hBOOL(hAPP(hAPP(X2339,X2340),X2338)) )
& ( ~ hBOOL(hAPP(hAPP(X2339,X2340),X2338))
| c_member(X2341,X2340,c_SetInterval_Oord_OlessThan(X2341,X2339,X2338)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])]) ).
fof(i_0_748,plain,
! [X2330,X2331,X2332,X2333] :
( ( ~ c_member(X2333,X2332,c_SetInterval_Oord_OatMost(X2333,X2331,X2330))
| hBOOL(hAPP(hAPP(X2331,X2332),X2330)) )
& ( ~ hBOOL(hAPP(hAPP(X2331,X2332),X2330))
| c_member(X2333,X2332,c_SetInterval_Oord_OatMost(X2333,X2331,X2330)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])]) ).
fof(i_0_749,plain,
! [X2342,X2343,X2344,X2345] :
( ( ~ c_member(X2345,X2344,c_SetInterval_Oord_OgreaterThan(X2345,X2343,X2342))
| hBOOL(hAPP(hAPP(X2343,X2342),X2344)) )
& ( ~ hBOOL(hAPP(hAPP(X2343,X2342),X2344))
| c_member(X2345,X2344,c_SetInterval_Oord_OgreaterThan(X2345,X2343,X2342)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])]) ).
fof(i_0_750,plain,
! [X2334,X2335,X2336,X2337] :
( ( ~ c_member(X2337,X2336,c_SetInterval_Oord_OatLeast(X2337,X2335,X2334))
| hBOOL(hAPP(hAPP(X2335,X2334),X2336)) )
& ( ~ hBOOL(hAPP(hAPP(X2335,X2334),X2336))
| c_member(X2337,X2336,c_SetInterval_Oord_OatLeast(X2337,X2335,X2334)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])]) ).
fof(i_0_751,plain,
! [X2770,X2771] :
( ( ~ c_Orderings_Oord__class_Oless(X2771,c_Groups_Ozero__class_Ozero(X2771),c_Groups_Oplus__class_Oplus(X2771,X2770,X2770))
| c_Orderings_Oord__class_Oless(X2771,c_Groups_Ozero__class_Ozero(X2771),X2770)
| ~ class_Groups_Olinordered__ab__group__add(X2771) )
& ( ~ c_Orderings_Oord__class_Oless(X2771,c_Groups_Ozero__class_Ozero(X2771),X2770)
| c_Orderings_Oord__class_Oless(X2771,c_Groups_Ozero__class_Ozero(X2771),c_Groups_Oplus__class_Oplus(X2771,X2770,X2770))
| ~ class_Groups_Olinordered__ab__group__add(X2771) ) ),
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_752,plain,
! [X2750,X2751] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2751,c_Groups_Ozero__class_Ozero(X2751),c_Groups_Oplus__class_Oplus(X2751,X2750,X2750))
| c_Orderings_Oord__class_Oless__eq(X2751,c_Groups_Ozero__class_Ozero(X2751),X2750)
| ~ class_Groups_Olinordered__ab__group__add(X2751) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2751,c_Groups_Ozero__class_Ozero(X2751),X2750)
| c_Orderings_Oord__class_Oless__eq(X2751,c_Groups_Ozero__class_Ozero(X2751),c_Groups_Oplus__class_Oplus(X2751,X2750,X2750))
| ~ class_Groups_Olinordered__ab__group__add(X2751) ) ),
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_753,plain,
! [X2816,X2817] :
( ( ~ c_Orderings_Oord__class_Oless(X2817,c_Groups_Oplus__class_Oplus(X2817,X2816,X2816),c_Groups_Ozero__class_Ozero(X2817))
| c_Orderings_Oord__class_Oless(X2817,X2816,c_Groups_Ozero__class_Ozero(X2817))
| ~ class_Rings_Olinordered__idom(X2817) )
& ( ~ c_Orderings_Oord__class_Oless(X2817,X2816,c_Groups_Ozero__class_Ozero(X2817))
| c_Orderings_Oord__class_Oless(X2817,c_Groups_Oplus__class_Oplus(X2817,X2816,X2816),c_Groups_Ozero__class_Ozero(X2817))
| ~ class_Rings_Olinordered__idom(X2817) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_754,plain,
! [X2768,X2769] :
( ( ~ c_Orderings_Oord__class_Oless(X2769,c_Groups_Oplus__class_Oplus(X2769,X2768,X2768),c_Groups_Ozero__class_Ozero(X2769))
| c_Orderings_Oord__class_Oless(X2769,X2768,c_Groups_Ozero__class_Ozero(X2769))
| ~ class_Groups_Olinordered__ab__group__add(X2769) )
& ( ~ c_Orderings_Oord__class_Oless(X2769,X2768,c_Groups_Ozero__class_Ozero(X2769))
| c_Orderings_Oord__class_Oless(X2769,c_Groups_Oplus__class_Oplus(X2769,X2768,X2768),c_Groups_Ozero__class_Ozero(X2769))
| ~ class_Groups_Olinordered__ab__group__add(X2769) ) ),
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_755,plain,
! [X2748,X2749] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2749,c_Groups_Oplus__class_Oplus(X2749,X2748,X2748),c_Groups_Ozero__class_Ozero(X2749))
| c_Orderings_Oord__class_Oless__eq(X2749,X2748,c_Groups_Ozero__class_Ozero(X2749))
| ~ class_Groups_Olinordered__ab__group__add(X2749) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2749,X2748,c_Groups_Ozero__class_Ozero(X2749))
| c_Orderings_Oord__class_Oless__eq(X2749,c_Groups_Oplus__class_Oplus(X2749,X2748,X2748),c_Groups_Ozero__class_Ozero(X2749))
| ~ class_Groups_Olinordered__ab__group__add(X2749) ) ),
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_756,plain,
! [X2832,X2833,X2834,X2835] :
( ~ class_Rings_Ocomm__semiring__1(X2835)
| c_Groups_Oplus__class_Oplus(X2835,c_Groups_Oplus__class_Oplus(X2835,X2834,X2833),X2832) = c_Groups_Oplus__class_Oplus(X2835,c_Groups_Oplus__class_Oplus(X2835,X2834,X2832),X2833) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_757,plain,
! [X2836,X2837,X2838,X2839] :
( ~ class_Rings_Ocomm__semiring__1(X2839)
| c_Groups_Oplus__class_Oplus(X2839,c_Groups_Oplus__class_Oplus(X2839,X2838,X2837),X2836) = c_Groups_Oplus__class_Oplus(X2839,X2838,c_Groups_Oplus__class_Oplus(X2839,X2837,X2836)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_758,plain,
! [X2563,X2564,X2565,X2566] :
( ~ class_Groups_Oab__semigroup__add(X2566)
| c_Groups_Oplus__class_Oplus(X2566,c_Groups_Oplus__class_Oplus(X2566,X2565,X2564),X2563) = c_Groups_Oplus__class_Oplus(X2566,X2565,c_Groups_Oplus__class_Oplus(X2566,X2564,X2563)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_759,plain,
! [X2840,X2841,X2842,X2843] :
( ~ class_Rings_Ocomm__semiring__1(X2843)
| c_Groups_Oplus__class_Oplus(X2843,X2842,c_Groups_Oplus__class_Oplus(X2843,X2841,X2840)) = c_Groups_Oplus__class_Oplus(X2843,c_Groups_Oplus__class_Oplus(X2843,X2842,X2841),X2840) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_760,plain,
! [X2844,X2845,X2846,X2847] :
( ~ class_Rings_Ocomm__semiring__1(X2847)
| c_Groups_Oplus__class_Oplus(X2847,X2846,c_Groups_Oplus__class_Oplus(X2847,X2845,X2844)) = c_Groups_Oplus__class_Oplus(X2847,X2845,c_Groups_Oplus__class_Oplus(X2847,X2846,X2844)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_761,plain,
! [X2239,X2240,X2241] : c_Set_Oimage(X2241,X2240,X2239,c_Orderings_Obot__class_Obot(tc_fun(X2241,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2240,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_image__empty]) ).
fof(i_0_762,plain,
! [X3143,X3144,X3145,X3146,X3147] :
( ~ c_Finite__Set_Ofolding__one__idem(X3147,X3146,X3145)
| ~ c_Finite__Set_Ofinite(X3147,X3144)
| X3144 = c_Orderings_Obot__class_Obot(tc_fun(X3147,tc_HOL_Obool))
| hAPP(X3145,c_Set_Oinsert(X3147,X3143,X3144)) = hAPP(hAPP(X3146,X3143),hAPP(X3145,X3144)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem])]) ).
fof(i_0_763,plain,
! [X3085,X3086,X3087,X3088] : c_Set_Oinsert(X3088,X3087,c_Set_Oinsert(X3088,X3086,X3085)) = c_Set_Oinsert(X3088,X3086,c_Set_Oinsert(X3088,X3087,X3085)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
fof(i_0_764,plain,
! [X2356,X2357,X2358,X2359] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X2359,tc_HOL_Obool),X2358,X2357)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2359,tc_HOL_Obool),X2357,X2356)
| c_Orderings_Oord__class_Oless(tc_fun(X2359,tc_HOL_Obool),X2358,X2356) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).
fof(i_0_765,plain,
! [X2093,X2094,X2095,X2096] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2096,tc_HOL_Obool),X2095,X2094)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2096,tc_HOL_Obool),X2094,X2093)
| c_Orderings_Oord__class_Oless(tc_fun(X2096,tc_HOL_Obool),X2095,X2093) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_766,plain,
! [X2089,X2090,X2091,X2092] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X2092,tc_HOL_Obool),X2091,X2090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2092,tc_HOL_Obool),X2090,X2089)
| c_Orderings_Oord__class_Oless(tc_fun(X2092,tc_HOL_Obool),X2091,X2089) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_767,plain,
! [X2154,X2155,X2156,X2157] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2157,tc_HOL_Obool),X2156,X2155)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2157,tc_HOL_Obool),X2155,X2154)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2157,tc_HOL_Obool),X2156,X2154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_768,plain,
! [X3164,X3165] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3165,X3164)
| c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3165,hAPP(c_Nat_OSuc,X3164)) = c_Set_Oinsert(tc_Nat_Onat,X3164,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3165,X3164)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3165,X3164)
| c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3165,hAPP(c_Nat_OSuc,X3164)) = 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_530])]) ).
fof(i_0_769,plain,
! [X2554,X2555,X2556] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2556,X2555),X2554) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2556,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2555,X2554)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_770,plain,
! [X2551,X2552,X2553] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2553,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2552,X2551)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2552,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2553,X2551)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_771,plain,
! [X1961,X1962,X1963] :
( ~ c_Finite__Set_Ofinite(X1963,X1962)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1963,tc_HOL_Obool),X1961,X1962)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1963,X1962),c_Finite__Set_Ocard(X1963,X1961))
| X1961 = X1962 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).
fof(i_0_772,plain,
! [X3099,X3100,X3101,X3102] :
( ( ~ c_member(X3102,X3101,c_Set_Oinsert(X3102,X3100,X3099))
| X3101 = X3100
| c_member(X3102,X3101,X3099) )
& ( X3101 != X3100
| c_member(X3102,X3101,c_Set_Oinsert(X3102,X3100,X3099)) )
& ( ~ c_member(X3102,X3101,X3099)
| c_member(X3102,X3101,c_Set_Oinsert(X3102,X3100,X3099)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).
fof(i_0_773,plain,
! [X3025,X3026,X3027,X3028] :
( ~ c_member(X3028,X3027,c_Set_Oinsert(X3028,X3026,X3025))
| X3027 = X3026
| c_member(X3028,X3027,X3025) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).
fof(i_0_774,plain,
! [X2894,X2895,X2896] :
( ~ class_Groups_Ocomm__monoid__add(X2896)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2895,X2896,X2894,c_Orderings_Obot__class_Obot(tc_fun(X2895,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X2896) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oempty])]) ).
fof(i_0_775,plain,
! [X2891,X2892,X2893] :
( ~ class_Groups_Ocomm__monoid__add(X2893)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2892,X2893,X2891,c_Orderings_Obot__class_Obot(tc_fun(X2892,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X2893) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__empty])]) ).
fof(i_0_776,plain,
! [X3048,X3049,X3050,X3051] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3051,tc_HOL_Obool),X3050,X3049)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3051,tc_HOL_Obool),X3050,c_Set_Oinsert(X3051,X3048,X3049)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).
fof(i_0_777,plain,
! [X2644,X2645,X2646,X2647] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2647,X2646)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2645,X2646) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2647,X2644)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2645,X2644) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_778,plain,
! [X2648,X2649,X2650] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2650,X2649),X2648)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2650,X2648) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_779,plain,
! [X2621,X2622,X2623] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2623,X2621)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2623,X2622),X2621) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2622,X2621)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2623,X2622),X2621) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_531])])]) ).
fof(i_0_780,plain,
! [X2618,X2619,X2620] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2620,X2619),X2618)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2620,X2618) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_781,plain,
! [X2615,X2616,X2617] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2617,X2616),X2615)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2616,X2615) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_782,plain,
! [X1729,X1730,X1731] : c_Fun_Oinj__on(X1731,X1730,X1729,c_Orderings_Obot__class_Obot(tc_fun(X1731,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_inj__on__empty]) ).
fof(i_0_783,plain,
! [X2742,X2743,X2744] :
( ( X2743 = c_Groups_Ozero__class_Ozero(X2744)
| c_Groups_Oplus__class_Oplus(X2744,X2743,X2742) != c_Groups_Ozero__class_Ozero(X2744)
| ~ c_Orderings_Oord__class_Oless__eq(X2744,c_Groups_Ozero__class_Ozero(X2744),X2742)
| ~ c_Orderings_Oord__class_Oless__eq(X2744,c_Groups_Ozero__class_Ozero(X2744),X2743)
| ~ class_Groups_Oordered__comm__monoid__add(X2744) )
& ( X2742 = c_Groups_Ozero__class_Ozero(X2744)
| c_Groups_Oplus__class_Oplus(X2744,X2743,X2742) != c_Groups_Ozero__class_Ozero(X2744)
| ~ c_Orderings_Oord__class_Oless__eq(X2744,c_Groups_Ozero__class_Ozero(X2744),X2742)
| ~ c_Orderings_Oord__class_Oless__eq(X2744,c_Groups_Ozero__class_Ozero(X2744),X2743)
| ~ class_Groups_Oordered__comm__monoid__add(X2744) )
& ( X2743 != c_Groups_Ozero__class_Ozero(X2744)
| X2742 != c_Groups_Ozero__class_Ozero(X2744)
| c_Groups_Oplus__class_Oplus(X2744,X2743,X2742) = c_Groups_Ozero__class_Ozero(X2744)
| ~ c_Orderings_Oord__class_Oless__eq(X2744,c_Groups_Ozero__class_Ozero(X2744),X2742)
| ~ c_Orderings_Oord__class_Oless__eq(X2744,c_Groups_Ozero__class_Ozero(X2744),X2743)
| ~ class_Groups_Oordered__comm__monoid__add(X2744) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_784,plain,
! [X2097,X2098,X2099,X2100] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2099,X2100),X2098,X2097)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2099,X2100),X2098,X2097)
| ~ class_Orderings_Oord(X2100) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2099,X2100),X2097,X2098)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2099,X2100),X2098,X2097)
| ~ class_Orderings_Oord(X2100) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2099,X2100),X2098,X2097)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2099,X2100),X2097,X2098)
| c_Orderings_Oord__class_Oless(tc_fun(X2099,X2100),X2098,X2097)
| ~ class_Orderings_Oord(X2100) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_532])])]) ).
fof(i_0_785,plain,
! [X1685] :
( ~ c_Finite__Set_Ofinite(X1685,c_Orderings_Otop__class_Otop(tc_fun(X1685,tc_HOL_Obool)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1685,c_Orderings_Otop__class_Otop(tc_fun(X1685,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).
fof(i_0_786,plain,
! [X2778,X2779] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2779,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2779,X2778))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_787,plain,
! [X2780,X2781] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2781,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2780,X2781))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_788,plain,
! [X3103,X3104,X3105,X3106] :
( ( c_Set_Oinsert(X3106,X3105,X3104) != c_Set_Oinsert(X3106,X3105,X3103)
| X3104 = X3103
| c_member(X3106,X3105,X3103)
| c_member(X3106,X3105,X3104) )
& ( X3104 != X3103
| c_Set_Oinsert(X3106,X3105,X3104) = c_Set_Oinsert(X3106,X3105,X3103)
| c_member(X3106,X3105,X3103)
| c_member(X3106,X3105,X3104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_533])])]) ).
fof(i_0_789,plain,
! [X3022,X3023,X3024] :
( ~ c_Finite__Set_Ofinite(X3024,X3023)
| c_member(X3024,X3022,X3023)
| c_Finite__Set_Ocard(X3024,c_Set_Oinsert(X3024,X3022,X3023)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(X3024,X3023)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_534])]) ).
fof(i_0_790,plain,
! [X2490,X2491,X2492,X2493,X2494] :
( ~ c_Finite__Set_Ofolding__one__idem(X2494,X2493,X2492)
| ~ c_Finite__Set_Ofinite(X2494,X2491)
| ~ c_member(X2494,X2490,X2491)
| hAPP(hAPP(X2493,X2490),hAPP(X2492,X2491)) = hAPP(X2492,X2491) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem])]) ).
fof(i_0_791,plain,
! [X2875,X2876,X2877,X2878] :
( ~ class_Groups_Ocomm__monoid__add(X2878)
| c_Finite__Set_Ofinite(X2877,X2876)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2877,X2878,X2875,X2876) = c_Groups_Ozero__class_Ozero(X2878) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_535])]) ).
fof(i_0_792,plain,
! [X2871,X2872,X2873,X2874] :
( ~ class_Groups_Ocomm__monoid__add(X2874)
| c_Finite__Set_Ofinite(X2873,X2872)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2873,X2874,X2871,X2872) = c_Groups_Ozero__class_Ozero(X2874) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_536])]) ).
fof(i_0_793,plain,
! [X2512,X2513,X2514] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2514,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X2514,X2513),c_SetInterval_Oord__class_OgreaterThan(X2514,X2512))
| c_Orderings_Oord__class_Oless__eq(X2514,X2512,X2513)
| ~ class_Orderings_Olinorder(X2514) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2514,X2512,X2513)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2514,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X2514,X2513),c_SetInterval_Oord__class_OgreaterThan(X2514,X2512))
| ~ class_Orderings_Olinorder(X2514) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff])])]) ).
fof(i_0_794,plain,
! [X2201,X2202,X2203,X2204] :
( ~ c_member(X2204,X2203,X2202)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2204,tc_HOL_Obool),X2202,X2201)
| c_member(X2204,X2203,X2201) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_795,plain,
! [X2074,X2075,X2076,X2077] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X2077,tc_HOL_Obool),X2076,X2075)
| ~ c_member(X2077,X2074,X2076)
| c_member(X2077,X2074,X2075) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_796,plain,
! [X2205,X2206,X2207,X2208] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2208,tc_HOL_Obool),X2207,X2206)
| ~ c_member(X2208,X2205,X2207)
| c_member(X2208,X2205,X2206) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_797,plain,
! [X2197,X2198,X2199,X2200] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2200,tc_HOL_Obool),X2199,X2198)
| ~ c_member(X2200,X2197,X2199)
| c_member(X2200,X2197,X2198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_798,plain,
! [X2043,X2044,X2045,X2046] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2046,tc_HOL_Obool),X2045,X2044)
| ~ c_member(X2046,X2043,X2045)
| c_member(X2046,X2043,X2044) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_799,plain,
! [X3131,X3132,X3133,X3134] :
( ( X3133 = X3132
| c_SetInterval_Oord__class_OatLeastAtMost(X3134,X3133,X3132) != c_Set_Oinsert(X3134,X3131,c_Orderings_Obot__class_Obot(tc_fun(X3134,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X3134) )
& ( X3132 = X3131
| c_SetInterval_Oord__class_OatLeastAtMost(X3134,X3133,X3132) != c_Set_Oinsert(X3134,X3131,c_Orderings_Obot__class_Obot(tc_fun(X3134,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X3134) )
& ( X3133 != X3132
| X3132 != X3131
| c_SetInterval_Oord__class_OatLeastAtMost(X3134,X3133,X3132) = c_Set_Oinsert(X3134,X3131,c_Orderings_Obot__class_Obot(tc_fun(X3134,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X3134) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff])])]) ).
fof(i_0_800,plain,
! [X1665,X1666] :
( ~ c_Finite__Set_Ofinite(X1666,c_Orderings_Otop__class_Otop(tc_fun(X1666,tc_HOL_Obool)))
| c_Finite__Set_Ocard(X1666,X1665) != c_Finite__Set_Ocard(X1666,c_Orderings_Otop__class_Otop(tc_fun(X1666,tc_HOL_Obool)))
| X1665 = c_Orderings_Otop__class_Otop(tc_fun(X1666,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).
fof(i_0_801,plain,
! [X2782,X2783,X2785,X2786,X2787] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2783,X2782)
| X2782 = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2783,esk27_2(X2782,X2783))) )
& ( X2785 != hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2786,X2787))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2786,X2785) ) ),
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_802,plain,
! [X2106,X2107,X2108] :
( ~ c_Finite__Set_Ofinite(X2108,X2107)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2108,tc_HOL_Obool),X2106,X2107)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(X2108,X2106),c_Finite__Set_Ocard(X2108,X2107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).
fof(i_0_803,plain,
! [X1964,X1965,X1966] :
( ~ c_Finite__Set_Ofinite(X1966,X1965)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1966,tc_HOL_Obool),X1964,X1965)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1966,X1964),c_Finite__Set_Ocard(X1966,X1965)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).
fof(i_0_804,plain,
! [X3107,X3108,X3109,X3110] :
( ~ c_member(X3110,X3109,X3108)
| c_member(X3110,X3109,c_Set_Oinsert(X3110,X3107,X3108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).
fof(i_0_805,plain,
! [X3029,X3030,X3031,X3032] :
( ( ~ c_member(X3032,X3031,X3030)
| c_member(X3032,X3031,c_Set_Oinsert(X3032,X3029,X3030)) )
& ( X3031 != X3029
| c_member(X3032,X3031,c_Set_Oinsert(X3032,X3029,X3030)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_537])])]) ).
fof(i_0_806,plain,
! [X2624,X2625] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2625,X2624),X2625),
inference(variable_rename,[status(thm)],[i_0_538]) ).
fof(i_0_807,plain,
! [X2626,X2627] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2627,X2626),X2626),
inference(variable_rename,[status(thm)],[i_0_539]) ).
fof(i_0_808,plain,
! [X2145,X2146,X2147] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2145,tc_HOL_Obool),X2147,X2146)
| X2147 != X2146 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2145,tc_HOL_Obool),X2146,X2147)
| X2147 != X2146 )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2145,tc_HOL_Obool),X2147,X2146)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2145,tc_HOL_Obool),X2146,X2147)
| X2147 = X2146 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_809,plain,
! [X2069,X2070,X2071] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2071,tc_HOL_Obool),X2070,X2069)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2071,tc_HOL_Obool),X2069,X2070)
| X2070 = X2069 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_810,plain,
! [X2450,X2451,X2452] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2452,X2451)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2451,X2450)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2452),X2450) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_811,plain,
! [X3161,X3162,X3163] :
( ( ~ c_member(X3163,X3161,X3162)
| c_Finite__Set_Ocard(X3163,c_Set_Oinsert(X3163,X3161,X3162)) = c_Finite__Set_Ocard(X3163,X3162)
| ~ c_Finite__Set_Ofinite(X3163,X3162) )
& ( c_member(X3163,X3161,X3162)
| c_Finite__Set_Ocard(X3163,c_Set_Oinsert(X3163,X3161,X3162)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X3163,X3162))
| ~ c_Finite__Set_Ofinite(X3163,X3162) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_540])])]) ).
fof(i_0_812,plain,
! [X2409] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X2409),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(i_0_813,plain,
! [X1933,X1934,X1935,X1936,X1937] :
( ~ class_Orderings_Oord(X1937)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1936,X1937),X1935,X1934)
| c_Orderings_Oord__class_Oless__eq(X1937,hAPP(X1935,X1933),hAPP(X1934,X1933)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_814,plain,
! [X1827,X1828,X1829,X1830,X1831] :
( ~ class_Orderings_Oord(X1831)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1830,X1831),X1829,X1828)
| c_Orderings_Oord__class_Oless__eq(X1831,hAPP(X1829,X1827),hAPP(X1828,X1827)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_815,plain,
! [X2631,X2632,X2633] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2633,X2632)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2633,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2632,X2631)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_816,plain,
! [X2537,X2538,X2539] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2539,X2538)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2539,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2538,X2537)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_817,plain,
! [X2634,X2635,X2636] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2636,X2635)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2636,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2634,X2635)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_818,plain,
! [X2540,X2541,X2542] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2542,X2541)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2542,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2540,X2541)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_819,plain,
! [X2602,X2603,X2604] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2604,X2603)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2604,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2603,X2602)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_820,plain,
! [X2546,X2547,X2548] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2548,X2547)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2548,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2547,X2546)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_821,plain,
! [X2605,X2606,X2607] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2607,X2606)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2607,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2605,X2606)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_822,plain,
! [X2543,X2544,X2545] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2545,X2544)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2545,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2543,X2544)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_823,plain,
! [X3158,X3159,X3160] :
( ~ c_Finite__Set_Ofinite(X3160,X3159)
| c_member(X3160,X3158,X3159)
| c_Finite__Set_Ocard(X3160,c_Set_Oinsert(X3160,X3158,X3159)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X3160,X3159)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])]) ).
fof(i_0_824,plain,
! [X1884,X1885,X1886,X1887] :
( ~ class_Orderings_Opreorder(X1887)
| ~ c_Orderings_Oord__class_Oless(X1887,X1886,X1885)
| ~ c_Orderings_Oord__class_Oless(X1887,X1885,X1884)
| c_Orderings_Oord__class_Oless(X1887,X1886,X1884) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_825,plain,
! [X1908,X1909,X1910,X1911] :
( ~ class_Orderings_Opreorder(X1911)
| ~ c_Orderings_Oord__class_Oless__eq(X1911,X1910,X1909)
| ~ c_Orderings_Oord__class_Oless(X1911,X1909,X1908)
| c_Orderings_Oord__class_Oless(X1911,X1910,X1908) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_826,plain,
! [X1888,X1889,X1890,X1891] :
( ~ class_Orderings_Opreorder(X1891)
| ~ c_Orderings_Oord__class_Oless(X1891,X1890,X1889)
| ~ c_Orderings_Oord__class_Oless__eq(X1891,X1889,X1888)
| c_Orderings_Oord__class_Oless(X1891,X1890,X1888) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_827,plain,
! [X1892,X1893,X1894,X1895] :
( ~ class_Orderings_Oorder(X1895)
| ~ c_Orderings_Oord__class_Oless(X1895,X1894,X1893)
| ~ c_Orderings_Oord__class_Oless(X1895,X1892,X1894)
| c_Orderings_Oord__class_Oless(X1895,X1892,X1893) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_828,plain,
! [X1919,X1920,X1921,X1922] :
( ~ class_Orderings_Oorder(X1922)
| ~ c_Orderings_Oord__class_Oless__eq(X1922,X1921,X1920)
| ~ c_Orderings_Oord__class_Oless(X1922,X1919,X1921)
| c_Orderings_Oord__class_Oless(X1922,X1919,X1920) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_829,plain,
! [X1896,X1897,X1898,X1899] :
( ~ class_Orderings_Oorder(X1899)
| ~ c_Orderings_Oord__class_Oless(X1899,X1898,X1897)
| ~ c_Orderings_Oord__class_Oless__eq(X1899,X1896,X1898)
| c_Orderings_Oord__class_Oless(X1899,X1896,X1897) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_830,plain,
! [X1915,X1916,X1917,X1918] :
( ~ class_Orderings_Opreorder(X1918)
| ~ c_Orderings_Oord__class_Oless__eq(X1918,X1917,X1916)
| ~ c_Orderings_Oord__class_Oless__eq(X1918,X1916,X1915)
| c_Orderings_Oord__class_Oless__eq(X1918,X1917,X1915) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_831,plain,
! [X1926,X1927,X1928,X1929] :
( ~ class_Orderings_Oorder(X1929)
| ~ c_Orderings_Oord__class_Oless__eq(X1929,X1928,X1927)
| ~ c_Orderings_Oord__class_Oless__eq(X1929,X1926,X1928)
| c_Orderings_Oord__class_Oless__eq(X1929,X1926,X1927) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_832,plain,
! [X2232,X2233] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2233,tc_HOL_Obool),X2232,c_Orderings_Obot__class_Obot(tc_fun(X2233,tc_HOL_Obool)))
| X2232 = c_Orderings_Obot__class_Obot(tc_fun(X2233,tc_HOL_Obool)) )
& ( X2232 != c_Orderings_Obot__class_Obot(tc_fun(X2233,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2233,tc_HOL_Obool),X2232,c_Orderings_Obot__class_Obot(tc_fun(X2233,tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])]) ).
fof(i_0_833,plain,
! [X3166,X3167] : c_Set_Othe__elem(X3167,c_Set_Oinsert(X3167,X3166,c_Orderings_Obot__class_Obot(tc_fun(X3167,tc_HOL_Obool)))) = X3166,
inference(variable_rename,[status(thm)],[fact_the__elem__eq]) ).
fof(i_0_834,plain,
! [X2945,X2946,X2947] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2947,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2947,X2946,X2945)
| ~ c_Orderings_Oord__class_Oless__eq(X2947,X2946,X2945)
| ~ class_Orderings_Oorder(X2947) )
& ( c_Orderings_Oord__class_Oless__eq(X2947,X2946,X2945)
| c_Orderings_Obot__class_Obot(tc_fun(X2947,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2947,X2946,X2945)
| ~ class_Orderings_Oorder(X2947) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])])]) ).
fof(i_0_835,plain,
! [X2311,X2312,X2313] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2313,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastLessThan(X2313,X2312,X2311)
| ~ c_Orderings_Oord__class_Oless(X2313,X2312,X2311)
| ~ class_Orderings_Oorder(X2313) )
& ( c_Orderings_Oord__class_Oless(X2313,X2312,X2311)
| c_Orderings_Obot__class_Obot(tc_fun(X2313,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2313,X2312,X2311)
| ~ class_Orderings_Oorder(X2313) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])])]) ).
fof(i_0_836,plain,
! [X2942,X2943,X2944] :
( ( c_SetInterval_Oord__class_OatLeastAtMost(X2944,X2943,X2942) != c_Orderings_Obot__class_Obot(tc_fun(X2944,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(X2944,X2943,X2942)
| ~ class_Orderings_Oorder(X2944) )
& ( c_Orderings_Oord__class_Oless__eq(X2944,X2943,X2942)
| c_SetInterval_Oord__class_OatLeastAtMost(X2944,X2943,X2942) = c_Orderings_Obot__class_Obot(tc_fun(X2944,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X2944) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])])]) ).
fof(i_0_837,plain,
! [X2314,X2315,X2316] :
( ( c_SetInterval_Oord__class_OatLeastLessThan(X2316,X2315,X2314) != c_Orderings_Obot__class_Obot(tc_fun(X2316,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless(X2316,X2315,X2314)
| ~ class_Orderings_Oorder(X2316) )
& ( c_Orderings_Oord__class_Oless(X2316,X2315,X2314)
| c_SetInterval_Oord__class_OatLeastLessThan(X2316,X2315,X2314) = c_Orderings_Obot__class_Obot(tc_fun(X2316,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X2316) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])])]) ).
fof(i_0_838,plain,
! [X2166,X2167,X2168] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2168,X2167)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2167,X2166)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2168,X2166) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_839,plain,
! [X1649] :
( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X1649),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1649),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X1649,c_Orderings_Otop__class_Otop(tc_fun(X1649,tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X1649,c_Orderings_Otop__class_Otop(tc_fun(X1649,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X1649),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1649),tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).
fof(i_0_840,plain,
! [X3082,X3083,X3084] : c_Set_Oinsert(X3084,X3083,c_Set_Oinsert(X3084,X3083,X3082)) = c_Set_Oinsert(X3084,X3083,X3082),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
fof(i_0_841,plain,
! [X2457,X2458] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2458),hAPP(c_Nat_OSuc,X2457))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2458,X2457) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_842,plain,
! [X2440,X2441] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2441),hAPP(c_Nat_OSuc,X2440))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2441,X2440) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2441,X2440)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2441),hAPP(c_Nat_OSuc,X2440)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_843,plain,
! [X2428,X2429] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2429),hAPP(c_Nat_OSuc,X2428))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2429,X2428) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2429,X2428)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2429),hAPP(c_Nat_OSuc,X2428)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_844,plain,
! [X2478,X2479] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2478,hAPP(c_Nat_OSuc,X2479))
| X2478 = X2479
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2479,X2478) )
& ( X2478 != X2479
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2478,hAPP(c_Nat_OSuc,X2479))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2479,X2478) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_845,plain,
! [X3093,X3094,X3095] :
( ( ~ c_Finite__Set_Ofinite(X3095,c_Set_Oinsert(X3095,X3094,X3093))
| c_Finite__Set_Ofinite(X3095,X3093) )
& ( ~ c_Finite__Set_Ofinite(X3095,X3093)
| c_Finite__Set_Ofinite(X3095,c_Set_Oinsert(X3095,X3094,X3093)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).
fof(i_0_846,plain,
! [X2424,X2425] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2425,X2424)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2424),X2425) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2424),X2425)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2425,X2424) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])]) ).
fof(i_0_847,plain,
! [X2436,X2437] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2437,X2436)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2436,hAPP(c_Nat_OSuc,X2437)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2436,hAPP(c_Nat_OSuc,X2437))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2437,X2436) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])]) ).
fof(i_0_848,plain,
! [X2078,X2079] : ~ c_Orderings_Oord__class_Oless(tc_fun(X2079,tc_HOL_Obool),X2078,c_Orderings_Obot__class_Obot(tc_fun(X2079,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[i_0_548]) ).
fof(i_0_849,plain,
! [X1766,X1767,X1768] :
( ( c_Orderings_Oord__class_Oless__eq(X1768,X1767,X1766)
| ~ c_Orderings_Oord__class_Oless(X1768,X1767,X1766)
| ~ class_Orderings_Opreorder(X1768) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1768,X1766,X1767)
| ~ c_Orderings_Oord__class_Oless(X1768,X1767,X1766)
| ~ class_Orderings_Opreorder(X1768) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1768,X1767,X1766)
| c_Orderings_Oord__class_Oless__eq(X1768,X1766,X1767)
| c_Orderings_Oord__class_Oless(X1768,X1767,X1766)
| ~ class_Orderings_Opreorder(X1768) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])])]) ).
fof(i_0_850,plain,
! [X2470,X2471,X2473,X2474,X2475] :
( ( X2471 = hAPP(c_Nat_OSuc,esk23_2(X2470,X2471))
| X2471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2471,hAPP(c_Nat_OSuc,X2470)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(X2470,X2471),X2470)
| X2471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2471,hAPP(c_Nat_OSuc,X2470)) )
& ( X2474 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2474,hAPP(c_Nat_OSuc,X2473)) )
& ( X2474 != hAPP(c_Nat_OSuc,X2475)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2475,X2473)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2474,hAPP(c_Nat_OSuc,X2473)) ) ),
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])])])])])]) ).
fof(i_0_851,plain,
! [X2083,X2084,X2085] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2085,tc_HOL_Obool),X2084,X2083)
| c_Orderings_Oord__class_Oless(tc_fun(X2085,tc_HOL_Obool),X2084,X2083)
| X2084 = X2083 )
& ( ~ c_Orderings_Oord__class_Oless(tc_fun(X2085,tc_HOL_Obool),X2084,X2083)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2085,tc_HOL_Obool),X2084,X2083) )
& ( X2084 != X2083
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2085,tc_HOL_Obool),X2084,X2083) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_852,plain,
! [X2080,X2081,X2082] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2082,tc_HOL_Obool),X2081,X2080)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2082,tc_HOL_Obool),X2081,X2080) )
& ( X2081 != X2080
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2082,tc_HOL_Obool),X2081,X2080) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2082,tc_HOL_Obool),X2081,X2080)
| X2081 = X2080
| c_Orderings_Oord__class_Oless(tc_fun(X2082,tc_HOL_Obool),X2081,X2080) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_853,plain,
! [X3015,X3016] :
( ( c_Groups_Oplus__class_Oplus(X3016,X3015,X3015) != c_Groups_Ozero__class_Ozero(X3016)
| X3015 = c_Groups_Ozero__class_Ozero(X3016)
| ~ c_member(X3016,X3015,c_Int_Oring__1__class_OInts(X3016))
| ~ class_Int_Oring__char__0(X3016) )
& ( X3015 != c_Groups_Ozero__class_Ozero(X3016)
| c_Groups_Oplus__class_Oplus(X3016,X3015,X3015) = c_Groups_Ozero__class_Ozero(X3016)
| ~ c_member(X3016,X3015,c_Int_Oring__1__class_OInts(X3016))
| ~ class_Int_Oring__char__0(X3016) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).
fof(i_0_854,plain,
! [X1850,X1851,X1852,X1853] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1853,tc_HOL_Obool),X1852,X1851)
| ~ hBOOL(hAPP(X1852,X1850))
| hBOOL(hAPP(X1851,X1850)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_855,plain,
! [X1802,X1803,X1804,X1805] :
( ~ hBOOL(hAPP(X1805,X1804))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1803,tc_HOL_Obool),X1805,X1802)
| hBOOL(hAPP(X1802,X1804)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_856,plain,
! [X2086,X2087,X2088] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X2088,tc_HOL_Obool),X2087,X2086)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2088,tc_HOL_Obool),X2087,X2086) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_857,plain,
! [X2996] :
( ~ class_Rings_Olinordered__semidom(X2996)
| c_Orderings_Oord__class_Oless(X2996,c_Groups_Ozero__class_Ozero(X2996),c_Groups_Oplus__class_Oplus(X2996,c_Groups_Oone__class_Oone(X2996),c_Groups_Oone__class_Oone(X2996))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_858,plain,
! [X2727,X2728] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2728),X2727) = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2728,X2727)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_859,plain,
! [X2729,X2730] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2730,hAPP(c_Nat_OSuc,X2729)) = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2730,X2729)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_860,plain,
! [X2134,X2135,X2136] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2135,X2136)
| hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| X2136 = X2135
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2136,X2135) )
& ( ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| X2136 = X2135
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2136,X2135) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2135,X2136)
| hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2136,X2135) )
& ( ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2136,X2135) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2135,X2136)
| hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| X2136 = X2135
| ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136)) )
& ( ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| X2136 = X2135
| ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2135,X2136)
| hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136)) )
& ( ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136))
| ~ hBOOL(hAPP(hAPP(X2134,X2135),X2136)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_861,plain,
! [X2509,X2510,X2511] :
( ( ~ c_member(X2511,X2510,c_SetInterval_Oord__class_OgreaterThan(X2511,X2509))
| c_Orderings_Oord__class_Oless(X2511,X2509,X2510)
| ~ class_Orderings_Oord(X2511) )
& ( ~ c_Orderings_Oord__class_Oless(X2511,X2509,X2510)
| c_member(X2511,X2510,c_SetInterval_Oord__class_OgreaterThan(X2511,X2509))
| ~ class_Orderings_Oord(X2511) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])]) ).
fof(i_0_862,plain,
! [X2432,X2433] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2433,hAPP(c_Nat_OSuc,X2432))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2433,X2432)
| X2433 = hAPP(c_Nat_OSuc,X2432) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])]) ).
fof(i_0_863,plain,
! [X2426,X2427] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2427,hAPP(c_Nat_OSuc,X2426))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2427,X2426)
| X2427 = hAPP(c_Nat_OSuc,X2426) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2427,X2426)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2427,hAPP(c_Nat_OSuc,X2426)) )
& ( X2427 != hAPP(c_Nat_OSuc,X2426)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2427,hAPP(c_Nat_OSuc,X2426)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_864,plain,
! [X3052,X3053,X3054] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3054,tc_HOL_Obool),X3053,c_Set_Oinsert(X3054,X3052,X3053)),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(i_0_865,plain,
! [X1824,X1825,X1826] :
( ( c_Orderings_Oord__class_Oless(X1826,X1825,X1824)
| X1825 = X1824
| ~ c_Orderings_Oord__class_Oless__eq(X1826,X1825,X1824)
| ~ class_Orderings_Olinorder(X1826) )
& ( X1825 != X1824
| ~ c_Orderings_Oord__class_Oless(X1826,X1825,X1824)
| ~ c_Orderings_Oord__class_Oless__eq(X1826,X1825,X1824)
| ~ class_Orderings_Olinorder(X1826) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])])]) ).
fof(i_0_866,plain,
! [X2399,X2400] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2400,X2399)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2400),hAPP(c_Nat_OSuc,X2399)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_867,plain,
! [X1923,X1924,X1925] :
( ~ class_Orderings_Oorder(X1925)
| ~ c_Orderings_Oord__class_Oless__eq(X1925,X1924,X1923)
| ~ c_Orderings_Oord__class_Oless__eq(X1925,X1923,X1924)
| X1923 = X1924 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_868,plain,
! [X1912,X1913,X1914] :
( ~ class_Orderings_Oorder(X1914)
| ~ c_Orderings_Oord__class_Oless__eq(X1914,X1913,X1912)
| ~ c_Orderings_Oord__class_Oless__eq(X1914,X1912,X1913)
| X1913 = X1912 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_869,plain,
! [X1841,X1842,X1843] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X1843,X1841,X1842)
| X1841 = X1842
| ~ c_Orderings_Oord__class_Oless__eq(X1843,X1842,X1841)
| ~ class_Orderings_Oorder(X1843) )
& ( X1841 != X1842
| c_Orderings_Oord__class_Oless__eq(X1843,X1841,X1842)
| ~ c_Orderings_Oord__class_Oless__eq(X1843,X1842,X1841)
| ~ class_Orderings_Oorder(X1843) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_870,plain,
! [X1769,X1770,X1771] :
( ( c_Orderings_Oord__class_Oless__eq(X1771,X1770,X1769)
| X1770 != X1769
| ~ class_Orderings_Oorder(X1771) )
& ( c_Orderings_Oord__class_Oless__eq(X1771,X1769,X1770)
| X1770 != X1769
| ~ class_Orderings_Oorder(X1771) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1771,X1770,X1769)
| ~ c_Orderings_Oord__class_Oless__eq(X1771,X1769,X1770)
| X1770 = X1769
| ~ class_Orderings_Oorder(X1771) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_871,plain,
! [X2984,X2985] :
( ~ class_Rings_Olinordered__semidom(X2985)
| c_Orderings_Oord__class_Oless(X2985,X2984,c_Groups_Oplus__class_Oplus(X2985,X2984,c_Groups_Oone__class_Oone(X2985))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_872,plain,
! [X2583,X2584,X2585,X2586] :
( ~ class_Groups_Ocancel__semigroup__add(X2586)
| c_Groups_Oplus__class_Oplus(X2586,X2585,X2584) != c_Groups_Oplus__class_Oplus(X2586,X2583,X2584)
| X2585 = X2583 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_873,plain,
! [X2571,X2572,X2573,X2574] :
( ( c_Groups_Oplus__class_Oplus(X2574,X2573,X2572) != c_Groups_Oplus__class_Oplus(X2574,X2571,X2572)
| X2573 = X2571
| ~ class_Groups_Ocancel__semigroup__add(X2574) )
& ( X2573 != X2571
| c_Groups_Oplus__class_Oplus(X2574,X2573,X2572) = c_Groups_Oplus__class_Oplus(X2574,X2571,X2572)
| ~ class_Groups_Ocancel__semigroup__add(X2574) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_874,plain,
! [X2579,X2580,X2581,X2582] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X2582)
| c_Groups_Oplus__class_Oplus(X2582,X2581,X2580) != c_Groups_Oplus__class_Oplus(X2582,X2581,X2579)
| X2580 = X2579 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_875,plain,
! [X2575,X2576,X2577,X2578] :
( ~ class_Groups_Ocancel__semigroup__add(X2578)
| c_Groups_Oplus__class_Oplus(X2578,X2577,X2576) != c_Groups_Oplus__class_Oplus(X2578,X2577,X2575)
| X2576 = X2575 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_876,plain,
! [X2567,X2568,X2569,X2570] :
( ( c_Groups_Oplus__class_Oplus(X2570,X2569,X2568) != c_Groups_Oplus__class_Oplus(X2570,X2569,X2567)
| X2568 = X2567
| ~ class_Groups_Ocancel__semigroup__add(X2570) )
& ( X2568 != X2567
| c_Groups_Oplus__class_Oplus(X2570,X2569,X2568) = c_Groups_Oplus__class_Oplus(X2570,X2569,X2567)
| ~ class_Groups_Ocancel__semigroup__add(X2570) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_877,plain,
! [X1857,X1858,X1859] :
( ~ class_Orderings_Oorder(X1859)
| ~ c_Orderings_Oord__class_Oless(X1859,X1858,X1857)
| ~ c_Orderings_Oord__class_Oless(X1859,X1857,X1858) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])]) ).
fof(i_0_878,plain,
! [X1748,X1749,X1750] :
( ( c_Orderings_Oord__class_Oless(X1750,X1749,X1748)
| c_Orderings_Oord__class_Oless(X1750,X1748,X1749)
| X1749 = X1748
| ~ class_Orderings_Olinorder(X1750) )
& ( ~ c_Orderings_Oord__class_Oless(X1750,X1748,X1749)
| ~ c_Orderings_Oord__class_Oless(X1750,X1749,X1748)
| ~ class_Orderings_Olinorder(X1750) )
& ( X1749 != X1748
| ~ c_Orderings_Oord__class_Oless(X1750,X1749,X1748)
| ~ class_Orderings_Olinorder(X1750) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])])]) ).
fof(i_0_879,plain,
! [X1812,X1813,X1814] :
( ~ class_Orderings_Olinorder(X1814)
| ~ c_Orderings_Oord__class_Oless__eq(X1814,X1813,X1812)
| ~ c_Orderings_Oord__class_Oless(X1814,X1812,X1813) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])]) ).
fof(i_0_880,plain,
! [X1739,X1740,X1741] :
( ( c_Orderings_Oord__class_Oless(X1741,X1740,X1739)
| c_Orderings_Oord__class_Oless__eq(X1741,X1739,X1740)
| ~ class_Orderings_Olinorder(X1741) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1741,X1739,X1740)
| ~ c_Orderings_Oord__class_Oless(X1741,X1740,X1739)
| ~ class_Orderings_Olinorder(X1741) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])])]) ).
fof(i_0_881,plain,
! [X1742,X1743,X1744] :
( ( c_Orderings_Oord__class_Oless__eq(X1744,X1743,X1742)
| c_Orderings_Oord__class_Oless(X1744,X1742,X1743)
| ~ class_Orderings_Olinorder(X1744) )
& ( ~ c_Orderings_Oord__class_Oless(X1744,X1742,X1743)
| ~ c_Orderings_Oord__class_Oless__eq(X1744,X1743,X1742)
| ~ class_Orderings_Olinorder(X1744) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])])]) ).
fof(i_0_882,plain,
! [X1930,X1931,X1932] :
( ~ class_Orderings_Opreorder(X1932)
| ~ c_Orderings_Oord__class_Oless(X1932,X1931,X1930)
| ~ c_Orderings_Oord__class_Oless(X1932,X1930,X1931) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])]) ).
fof(i_0_883,plain,
! [X1854,X1855,X1856] :
( ~ class_Orderings_Opreorder(X1856)
| ~ c_Orderings_Oord__class_Oless(X1856,X1855,X1854)
| ~ c_Orderings_Oord__class_Oless(X1856,X1854,X1855) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])]) ).
fof(i_0_884,plain,
! [X1821,X1822,X1823] :
( ~ class_Orderings_Opreorder(X1823)
| ~ c_Orderings_Oord__class_Oless(X1823,X1822,X1821)
| ~ c_Orderings_Oord__class_Oless(X1823,X1821,X1822) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])]) ).
fof(i_0_885,plain,
! [X1809,X1810,X1811] :
( ~ class_Orderings_Opreorder(X1811)
| ~ c_Orderings_Oord__class_Oless(X1811,X1810,X1809)
| ~ c_Orderings_Oord__class_Oless(X1811,X1809,X1810) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_560])]) ).
fof(i_0_886,plain,
! [X2453,X2454] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2454,hAPP(c_Nat_OSuc,X2453))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2454,X2453)
| X2454 = X2453 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])]) ).
fof(i_0_887,plain,
! [X2444,X2445] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2445,X2444)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2445,hAPP(c_Nat_OSuc,X2444))
| X2444 = X2445 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])]) ).
fof(i_0_888,plain,
! [X2442,X2443] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2443,hAPP(c_Nat_OSuc,X2442))
| X2443 = X2442
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2443,X2442) )
& ( X2443 != X2442
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2443,hAPP(c_Nat_OSuc,X2442))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2443,X2442) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])])]) ).
fof(i_0_889,plain,
! [X2438,X2439] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2439,hAPP(c_Nat_OSuc,X2438))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2439,X2438)
| X2439 = X2438 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2439,X2438)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2439,hAPP(c_Nat_OSuc,X2438)) )
& ( X2439 != X2438
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2439,hAPP(c_Nat_OSuc,X2438)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_890,plain,
! [X2939,X2940,X2941] :
( ~ class_Orderings_Oorder(X2941)
| ~ c_Orderings_Oord__class_Oless(X2941,X2940,X2939)
| c_SetInterval_Oord__class_OatLeastAtMost(X2941,X2939,X2940) = c_Orderings_Obot__class_Obot(tc_fun(X2941,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty])]) ).
fof(i_0_891,plain,
! [X2308,X2309,X2310] :
( ~ class_Orderings_Oorder(X2310)
| ~ c_Orderings_Oord__class_Oless__eq(X2310,X2309,X2308)
| c_SetInterval_Oord__class_OatLeastLessThan(X2310,X2308,X2309) = c_Orderings_Obot__class_Obot(tc_fun(X2310,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty])]) ).
fof(i_0_892,plain,
! [X3142] : c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3142,hAPP(c_Nat_OSuc,X3142)) = c_Set_Oinsert(tc_Nat_Onat,X3142,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_atLeastLessThan__singleton]) ).
fof(i_0_893,plain,
! [X2448,X2449] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2449,X2448)
| hAPP(c_Nat_OSuc,X2449) = X2448
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2449),X2448) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_894,plain,
! [X2004,X2005] :
( ( X2004 != c_Orderings_Obot__class_Obot(tc_fun(X2005,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2005,X2004)) )
& ( c_Finite__Set_Ofinite(X2005,X2004)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2005,X2004)) )
& ( X2004 = c_Orderings_Obot__class_Obot(tc_fun(X2005,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X2005,X2004)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2005,X2004)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])]) ).
fof(i_0_895,plain,
! [X2455,X2456] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2456),X2455)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2456,X2455) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_896,plain,
! [X2488,X2489] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2489,X2488)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2489),X2488) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2489),X2488)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2489,X2488) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_897,plain,
! [X2484,X2485] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2485),X2484)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2485,X2484) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2485,X2484)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2485),X2484) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_898,plain,
! [X2476,X2477] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2477),X2476)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2477,X2476) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_899,plain,
! [X2434,X2435] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2435),X2434)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2435,X2434) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_900,plain,
! [X2486,X2487] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2487,hAPP(c_Nat_OSuc,X2486))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2487,X2486) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2487,X2486)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2487,hAPP(c_Nat_OSuc,X2486)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_901,plain,
! [X3128,X3129,X3130] :
( ~ class_Orderings_Oorder(X3130)
| X3129 != X3128
| c_SetInterval_Oord__class_OatLeastAtMost(X3130,X3129,X3128) = c_Set_Oinsert(X3130,X3129,c_Orderings_Obot__class_Obot(tc_fun(X3130,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H])]) ).
fof(i_0_902,plain,
! [X2169,X2170] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2170,X2169)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2169,X2170)
| X2170 = X2169 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_903,plain,
! [X2560,X2561,X2562] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2562,X2561) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2560,X2561)
| X2562 = X2560 )
& ( X2562 != X2560
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2562,X2561) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2560,X2561) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_904,plain,
! [X2557,X2558,X2559] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2559,X2558) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2559,X2557)
| X2558 = X2557 )
& ( X2558 != X2557
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2559,X2558) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2559,X2557) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_905,plain,
! [X3135,X3136] :
( ~ class_Orderings_Oorder(X3136)
| c_SetInterval_Oord__class_OatLeastAtMost(X3136,X3135,X3135) = c_Set_Oinsert(X3136,X3135,c_Orderings_Obot__class_Obot(tc_fun(X3136,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton])]) ).
fof(i_0_906,plain,
! [X2192,X2193] : ~ c_member(X2193,X2192,c_Orderings_Obot__class_Obot(tc_fun(X2193,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[i_0_564]) ).
fof(i_0_907,plain,
! [X2047,X2048] : ~ c_member(X2048,X2047,c_Orderings_Obot__class_Obot(tc_fun(X2048,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[i_0_565]) ).
fof(i_0_908,plain,
! [X2593,X2594,X2596,X2597,X2598] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2594,X2593)
| X2593 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2594,esk26_2(X2593,X2594)) )
& ( X2596 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2597,X2598)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2597,X2596) ) ),
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_909,plain,
! [X2137,X2139,X2140,X2141] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2137)
| ~ c_member(tc_Nat_Onat,X2139,X2137)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2139,esk12_1(X2137)) )
& ( c_member(tc_Nat_Onat,esk13_2(X2140,X2141),X2140)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X2140) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk13_2(X2140,X2141),X2141)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X2140) ) ),
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_910,plain,
! [X2171,X2173,X2174,X2175] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2171)
| ~ c_member(tc_Nat_Onat,X2173,X2171)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2173,esk14_1(X2171)) )
& ( c_member(tc_Nat_Onat,esk15_2(X2174,X2175),X2174)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X2174) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk15_2(X2174,X2175),X2175)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X2174) ) ),
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_911,plain,
! [X3096,X3097,X3098] : c_member(X3098,X3097,c_Set_Oinsert(X3098,X3097,X3096)),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
fof(i_0_912,plain,
! [X2480,X2481] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2481,X2480)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2481),X2480) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_913,plain,
! [X2446,X2447] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2447,X2446)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2447,hAPP(c_Nat_OSuc,X2446)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_914,plain,
! [X2482,X2483] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2483,X2482)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2483,hAPP(c_Nat_OSuc,X2482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_915,plain,
! [X2430,X2431] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2431,X2430)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2431,hAPP(c_Nat_OSuc,X2430)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_916,plain,
! [X1967,X1968,X1969] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1969,tc_HOL_Obool),X1968,X1967)
| ~ c_Finite__Set_Ofinite(X1969,X1967)
| c_Finite__Set_Ofinite(X1969,X1968) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).
fof(i_0_917,plain,
! [X1970,X1971,X1972] :
( ~ c_Finite__Set_Ofinite(X1972,X1971)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1972,tc_HOL_Obool),X1970,X1971)
| c_Finite__Set_Ofinite(X1972,X1970) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).
fof(i_0_918,plain,
! [X2591,X2592] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2592,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2592,X2591)),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_919,plain,
! [X2589,X2590] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2590,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2589,X2590)),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_920,plain,
! [X2725,X2726] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2726),X2725) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2726,hAPP(c_Nat_OSuc,X2725)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_921,plain,
! [X1847,X1848,X1849] :
( ~ class_Orderings_Oorder(X1849)
| ~ c_Orderings_Oord__class_Oless__eq(X1849,X1848,X1847)
| X1847 = X1848
| c_Orderings_Oord__class_Oless(X1849,X1848,X1847) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_922,plain,
! [X1844,X1845,X1846] :
( ~ class_Orderings_Oorder(X1846)
| ~ c_Orderings_Oord__class_Oless__eq(X1846,X1845,X1844)
| X1845 = X1844
| c_Orderings_Oord__class_Oless(X1846,X1845,X1844) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_923,plain,
! [X1838,X1839,X1840] :
( ~ class_Orderings_Oorder(X1840)
| ~ c_Orderings_Oord__class_Oless__eq(X1840,X1839,X1838)
| c_Orderings_Oord__class_Oless(X1840,X1839,X1838)
| X1839 = X1838 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_924,plain,
! [X1793,X1794,X1795] :
( ~ class_Orderings_Oorder(X1795)
| X1794 = X1793
| ~ c_Orderings_Oord__class_Oless__eq(X1795,X1794,X1793)
| c_Orderings_Oord__class_Oless(X1795,X1794,X1793) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_925,plain,
! [X1772,X1773,X1774] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X1774,X1773,X1772)
| c_Orderings_Oord__class_Oless(X1774,X1773,X1772)
| X1773 = X1772
| ~ class_Orderings_Oorder(X1774) )
& ( ~ c_Orderings_Oord__class_Oless(X1774,X1773,X1772)
| c_Orderings_Oord__class_Oless__eq(X1774,X1773,X1772)
| ~ class_Orderings_Oorder(X1774) )
& ( X1773 != X1772
| c_Orderings_Oord__class_Oless__eq(X1774,X1773,X1772)
| ~ class_Orderings_Oorder(X1774) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_926,plain,
! [X1763,X1764,X1765] :
( ( c_Orderings_Oord__class_Oless__eq(X1765,X1764,X1763)
| ~ c_Orderings_Oord__class_Oless(X1765,X1764,X1763)
| ~ class_Orderings_Oorder(X1765) )
& ( X1764 != X1763
| ~ c_Orderings_Oord__class_Oless(X1765,X1764,X1763)
| ~ class_Orderings_Oorder(X1765) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1765,X1764,X1763)
| X1764 = X1763
| c_Orderings_Oord__class_Oless(X1765,X1764,X1763)
| ~ class_Orderings_Oorder(X1765) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_927,plain,
! [X1790,X1791,X1792] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X1792,X1791,X1790)
| X1791 = X1790
| c_Orderings_Oord__class_Oless(X1792,X1791,X1790)
| ~ class_Orderings_Olinorder(X1792) )
& ( X1791 != X1790
| c_Orderings_Oord__class_Oless__eq(X1792,X1791,X1790)
| c_Orderings_Oord__class_Oless(X1792,X1791,X1790)
| ~ class_Orderings_Olinorder(X1792) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])])]) ).
fof(i_0_928,plain,
! [X1796,X1797,X1798] :
( ~ class_Orderings_Oorder(X1798)
| X1797 = X1796
| ~ c_Orderings_Oord__class_Oless__eq(X1798,X1796,X1797)
| c_Orderings_Oord__class_Oless(X1798,X1796,X1797) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_929,plain,
! [X1818,X1819,X1820] :
( ~ class_Orderings_Opreorder(X1820)
| ~ c_Orderings_Oord__class_Oless(X1820,X1819,X1818)
| c_Orderings_Oord__class_Oless__eq(X1820,X1819,X1818) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_930,plain,
! [X3033,X3034,X3035] :
( ~ c_Finite__Set_Ofinite(X3035,X3034)
| c_Finite__Set_Ofinite(X3035,c_Set_Oinsert(X3035,X3033,X3034)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).
fof(i_0_931,plain,
! [X2017,X2018] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2018,X2017))
| c_Finite__Set_Ofinite(X2018,X2017) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).
fof(i_0_932,plain,
! [X3111,X3112,X3113] :
( ~ c_member(X3113,X3112,X3111)
| c_Set_Oinsert(X3113,X3112,X3111) = X3111 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(i_0_933,plain,
! [X2774,X2775] :
( ( X2775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2775 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2775,X2774) )
& ( X2774 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2775 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2775,X2774) )
& ( X2775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2774 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2775,X2774) )
& ( X2774 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2774 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2775,X2774) )
& ( X2775 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2774 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2775,X2774) )
& ( X2775 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2774 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2775,X2774) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_934,plain,
! [X2772,X2773] :
( ( X2773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2773 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2773,X2772) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2772 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2773 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2773,X2772) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2772 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2773,X2772) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2772 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2772 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2773,X2772) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2773 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2772 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2773,X2772) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2773 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2772 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2773,X2772) = 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_935,plain,
! [X2897] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2897)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,X2897),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_nat_Osize_I4_J]) ).
fof(i_0_936,plain,
! [X2279,X2280] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2280,X2279)
| X2280 = X2279
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2280,X2279) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_937,plain,
! [X2275,X2276] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2276,X2275)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2276,X2275)
| X2276 = X2275 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2276,X2275)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2276,X2275) )
& ( X2276 != X2275
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2276,X2275) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_938,plain,
! [X2273,X2274] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2274,X2273)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2274,X2273) )
& ( X2274 != X2273
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2274,X2273) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2274,X2273)
| X2274 = X2273
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2274,X2273) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_939,plain,
! [X2372,X2373] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2373,X2372)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2373,X2372) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_940,plain,
! [X2281,X2282] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2282,X2281)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2282,X2281) )
& ( X2282 != X2281
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2282,X2281) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_941,plain,
! [X2277,X2278] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2278,X2277)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2278,X2277) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_942,plain,
! [X1614,X1615] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1615,tc_HOL_Obool)),X1614)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(i_0_943,plain,
! [X2469] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2469,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X2469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2469 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2469,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_944,plain,
! [X2194,X2195,X2196] :
( X2196 != c_Orderings_Obot__class_Obot(tc_fun(X2195,tc_HOL_Obool))
| ~ c_member(X2195,X2194,X2196) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).
fof(i_0_945,plain,
! [X2180,X2181,X2183,X2184,X2185] :
( ( c_member(X2181,esk16_2(X2180,X2181),X2180)
| X2180 = c_Orderings_Obot__class_Obot(tc_fun(X2181,tc_HOL_Obool)) )
& ( X2183 != c_Orderings_Obot__class_Obot(tc_fun(X2184,tc_HOL_Obool))
| ~ c_member(X2184,X2185,X2183) ) ),
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_568])])])])]) ).
fof(i_0_946,plain,
! [X2186,X2187,X2188,X2189,X2190] :
( ( ~ c_member(X2187,X2188,X2186)
| X2186 != c_Orderings_Obot__class_Obot(tc_fun(X2187,tc_HOL_Obool)) )
& ( X2189 = c_Orderings_Obot__class_Obot(tc_fun(X2190,tc_HOL_Obool))
| c_member(X2190,esk17_2(X2189,X2190),X2189) ) ),
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_947,plain,
! [X2033,X2034] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2034,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X2034,tc_HOL_Obool)),X2033),
inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).
fof(i_0_948,plain,
! [X2252,X2253] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2253,tc_HOL_Obool),X2252,c_Orderings_Otop__class_Otop(tc_fun(X2253,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(i_0_949,plain,
! [X2948,X2949] : c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2949,hAPP(c_Nat_OSuc,X2948)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2949,X2948),
inference(variable_rename,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost]) ).
fof(i_0_950,plain,
! [X3125,X3126,X3127] : c_Orderings_Obot__class_Obot(tc_fun(X3127,tc_HOL_Obool)) != c_Set_Oinsert(X3127,X3126,X3125),
inference(variable_rename,[status(thm)],[fact_empty__not__insert]) ).
fof(i_0_951,plain,
! [X3122,X3123,X3124] : c_Set_Oinsert(X3124,X3123,X3122) != c_Orderings_Obot__class_Obot(tc_fun(X3124,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_insert__not__empty]) ).
fof(i_0_952,plain,
! [X1602,X1603] :
( hAPP(X1603,esk1_2(X1602,X1603)) != hAPP(X1602,esk1_2(X1602,X1603))
| X1603 = X1602 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_953,plain,
! [X2410,X2411,X2412,X2413] :
( ~ c_Finite__Set_Ofolding__one__idem(X2413,X2412,X2411)
| hAPP(hAPP(X2412,X2410),X2410) = X2410 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem])]) ).
fof(i_0_954,plain,
! [X3019,X3020] :
( ( c_member(X3020,esk42_2(X3019,X3020),X3019)
| c_Finite__Set_Ocard(X3020,X3019) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X3020,X3019) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Finite__Set_Ocard(X3020,X3019) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X3020,X3019) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oneutral])])])]) ).
fof(i_0_955,plain,
! [X2423] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2423),X2423),
inference(variable_rename,[status(thm)],[i_0_569]) ).
fof(i_0_956,plain,
! [X1745,X1746,X1747] :
( ( X1746 = X1745
| c_Orderings_Oord__class_Oless(X1747,X1746,X1745)
| c_Orderings_Oord__class_Oless(X1747,X1745,X1746)
| ~ class_Orderings_Olinorder(X1747) )
& ( ~ c_Orderings_Oord__class_Oless(X1747,X1746,X1745)
| X1746 != X1745
| ~ class_Orderings_Olinorder(X1747) )
& ( ~ c_Orderings_Oord__class_Oless(X1747,X1745,X1746)
| X1746 != X1745
| ~ class_Orderings_Olinorder(X1747) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_957,plain,
! [X2820,X2821,X2822] :
( ~ class_Rings_Olinordered__idom(X2822)
| X2821 = X2820
| c_Orderings_Oord__class_Oless(X2822,X2821,X2820)
| c_Orderings_Oord__class_Oless(X2822,X2820,X2821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])]) ).
fof(i_0_958,plain,
! [X1941,X1942,X1943] :
( ~ class_Orderings_Olinorder(X1943)
| c_Orderings_Oord__class_Oless(X1943,X1942,X1941)
| X1942 = X1941
| c_Orderings_Oord__class_Oless(X1943,X1941,X1942) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])]) ).
fof(i_0_959,plain,
! [X1799,X1800,X1801] :
( ~ class_Orderings_Olinorder(X1801)
| X1800 = X1799
| c_Orderings_Oord__class_Oless(X1801,X1800,X1799)
| c_Orderings_Oord__class_Oless(X1801,X1799,X1800) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_572])]) ).
fof(i_0_960,plain,
! [X1787,X1788,X1789] :
( ( c_Orderings_Oord__class_Oless(X1789,X1787,X1788)
| X1787 = X1788
| c_Orderings_Oord__class_Oless(X1789,X1788,X1787)
| ~ class_Orderings_Olinorder(X1789) )
& ( X1787 != X1788
| ~ c_Orderings_Oord__class_Oless(X1789,X1787,X1788)
| c_Orderings_Oord__class_Oless(X1789,X1788,X1787)
| ~ class_Orderings_Olinorder(X1789) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_573])])]) ).
fof(i_0_961,plain,
! [X1775,X1776,X1777] :
( ~ class_Orderings_Olinorder(X1777)
| c_Orderings_Oord__class_Oless(X1777,X1776,X1775)
| X1776 = X1775
| c_Orderings_Oord__class_Oless(X1777,X1775,X1776) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_962,plain,
! [X1784,X1785,X1786] :
( ~ class_Orderings_Olinorder(X1786)
| c_Orderings_Oord__class_Oless__eq(X1786,X1785,X1784)
| c_Orderings_Oord__class_Oless(X1786,X1784,X1785) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_574])]) ).
fof(i_0_963,plain,
! [X1757,X1758,X1759] :
( ~ class_Orderings_Olinorder(X1759)
| c_Orderings_Oord__class_Oless__eq(X1759,X1758,X1757)
| c_Orderings_Oord__class_Oless(X1759,X1757,X1758) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_964,plain,
! [X1781,X1782,X1783] :
( ~ class_Orderings_Olinorder(X1783)
| c_Orderings_Oord__class_Oless(X1783,X1782,X1781)
| c_Orderings_Oord__class_Oless__eq(X1783,X1781,X1782) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_575])]) ).
fof(i_0_965,plain,
! [X1938,X1939,X1940] :
( ~ class_Orderings_Olinorder(X1940)
| c_Orderings_Oord__class_Oless__eq(X1940,X1939,X1938)
| c_Orderings_Oord__class_Oless__eq(X1940,X1938,X1939) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_576])]) ).
fof(i_0_966,plain,
! [X1760,X1761,X1762] :
( ~ class_Orderings_Olinorder(X1762)
| c_Orderings_Oord__class_Oless__eq(X1762,X1761,X1760)
| c_Orderings_Oord__class_Oless__eq(X1762,X1760,X1761) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_967,plain,
! [X2109,X2110,X2111] :
( ( ~ c_member(X2111,X2110,X2109)
| hBOOL(hAPP(X2109,X2110)) )
& ( ~ hBOOL(hAPP(X2109,X2110))
| c_member(X2111,X2110,X2109) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_968,plain,
! [X2932,X2933] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2933,X2932)),
inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost]) ).
fof(i_0_969,plain,
! [X2072,X2073] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2073,X2072)),
inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).
fof(i_0_970,plain,
! [X2848,X2849,X2850] :
( ~ class_Rings_Ocomm__semiring__1(X2850)
| c_Groups_Oplus__class_Oplus(X2850,X2849,X2848) = c_Groups_Oplus__class_Oplus(X2850,X2848,X2849) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_971,plain,
! [X2854] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X2854)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(X2854),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_972,plain,
! [X2988] :
( ~ class_Rings_Olinordered__semidom(X2988)
| ~ c_Orderings_Oord__class_Oless(X2988,c_Groups_Oone__class_Oone(X2988),c_Groups_Ozero__class_Ozero(X2988)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_577])]) ).
fof(i_0_973,plain,
! [X2986] :
( ~ class_Rings_Olinordered__semidom(X2986)
| ~ c_Orderings_Oord__class_Oless__eq(X2986,c_Groups_Oone__class_Oone(X2986),c_Groups_Ozero__class_Ozero(X2986)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_578])]) ).
fof(i_0_974,plain,
! [X2127,X2128] :
( X2128 = X2127
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2128,X2127)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2127,X2128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_579])]) ).
fof(i_0_975,plain,
! [X2125,X2126] :
( ( X2126 = X2125
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2126,X2125)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2125,X2126) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2126,X2125)
| X2126 != X2125 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2125,X2126)
| X2126 != X2125 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_976,plain,
! [X2465,X2467,X2468] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2465)
| X2465 = hAPP(c_Nat_OSuc,esk22_1(X2465)) )
& ( X2467 != hAPP(c_Nat_OSuc,X2468)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2467) ) ),
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_977,plain,
! [X2162,X2163] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2163,X2162)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2162,X2163) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_978,plain,
! [X2374,X2375] : c_member(X2375,X2374,c_Orderings_Otop__class_Otop(tc_fun(X2375,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(i_0_979,plain,
! [X2041,X2042] : c_member(X2042,X2041,c_Orderings_Otop__class_Otop(tc_fun(X2042,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(i_0_980,plain,
! [X2549,X2550] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2550,X2549) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2549,X2550),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_981,plain,
! [X2818,X2819] :
( ( c_Groups_Oplus__class_Oplus(X2819,X2818,X2818) != c_Groups_Ozero__class_Ozero(X2819)
| X2818 = c_Groups_Ozero__class_Ozero(X2819)
| ~ class_Groups_Olinordered__ab__group__add(X2819) )
& ( X2818 != c_Groups_Ozero__class_Ozero(X2819)
| c_Groups_Oplus__class_Oplus(X2819,X2818,X2818) = c_Groups_Ozero__class_Ozero(X2819)
| ~ class_Groups_Olinordered__ab__group__add(X2819) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_982,plain,
! [X2690,X2691] :
( ( c_Groups_Ozero__class_Ozero(X2691) != c_Groups_Oplus__class_Oplus(X2691,X2690,X2690)
| X2690 = c_Groups_Ozero__class_Ozero(X2691)
| ~ class_Groups_Olinordered__ab__group__add(X2691) )
& ( X2690 != c_Groups_Ozero__class_Ozero(X2691)
| c_Groups_Ozero__class_Ozero(X2691) = c_Groups_Oplus__class_Oplus(X2691,X2690,X2690)
| ~ class_Groups_Olinordered__ab__group__add(X2691) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_983,plain,
! [X2851,X2852,X2853] :
( ( X2852 != c_Groups_Oplus__class_Oplus(X2853,X2852,X2851)
| X2851 = c_Groups_Ozero__class_Ozero(X2853)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2853) )
& ( X2851 != c_Groups_Ozero__class_Ozero(X2853)
| X2852 = c_Groups_Oplus__class_Oplus(X2853,X2852,X2851)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2853) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_984,plain,
! [X1778,X1779,X1780] :
( ( ~ c_member(X1780,X1779,c_fequal(X1778))
| X1779 = X1778 )
& ( X1779 != X1778
| c_member(X1780,X1779,c_fequal(X1778)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_985,plain,
! [X1835,X1836,X1837] :
( ~ class_Orderings_Oorder(X1837)
| ~ c_Orderings_Oord__class_Oless(X1837,X1836,X1835)
| X1835 != X1836 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_986,plain,
! [X1832,X1833,X1834] :
( ~ class_Orderings_Oorder(X1834)
| ~ c_Orderings_Oord__class_Oless(X1834,X1833,X1832)
| X1833 != X1832 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_987,plain,
! [X1806,X1807,X1808] :
( ~ class_Orderings_Oorder(X1808)
| ~ c_Orderings_Oord__class_Oless(X1808,X1807,X1806)
| X1807 != X1806 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_988,plain,
! [X2250] :
( ( X2250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2250) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2250)
| X2250 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_989,plain,
! [X1732,X1733] :
( ~ class_Orderings_Opreorder(X1733)
| ~ c_Orderings_Oord__class_Oless(X1733,X1732,X1732) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_580])]) ).
fof(i_0_990,plain,
! [X2271] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2271,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2271 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2271 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2271,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_991,plain,
~ 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_992,plain,
! [X2653,X2654] :
( ( X2654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2654,X2653) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2653 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2654,X2653) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2654 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2653 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2654,X2653) = 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_993,plain,
! [X2247,X2248] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2248,X2247)
| X2247 != 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_994,plain,
! [X2651,X2652] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2652,X2651) != X2652
| X2651 = 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_995,plain,
! [X2251] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2251,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_581]) ).
fof(i_0_996,plain,
! [X2249] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2249,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_582]) ).
fof(i_0_997,plain,
! [X2032] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2032,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_583]) ).
fof(i_0_998,plain,
! [X2132,X2133] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2133,X2132)
| X2133 != X2132 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_999,plain,
! [X2130,X2131] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2131,X2130)
| X2130 != X2131 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_1000,plain,
! [X2234] : c_Orderings_Otop__class_Otop(tc_fun(X2234,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X2234,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__not__empty]) ).
fof(i_0_1001,plain,
! [X2129] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2129,X2129),
inference(variable_rename,[status(thm)],[i_0_584]) ).
fof(i_0_1002,plain,
! [X2124] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2124,X2124),
inference(variable_rename,[status(thm)],[i_0_585]) ).
fof(i_0_1003,plain,
! [X1736,X1737,X1738] :
( ~ class_Orderings_Obot(X1738)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1737,X1738)),X1736) = c_Orderings_Obot__class_Obot(X1738) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).
fof(i_0_1004,plain,
! [X1626,X1627,X1628] :
( ~ class_Orderings_Otop(X1628)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1627,X1628)),X1626) = c_Orderings_Otop__class_Otop(X1628) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).
fof(i_0_1005,plain,
! [X2158,X2159,X2160] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2158,tc_HOL_Obool),X2160,X2159)
| X2160 != X2159 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2158,tc_HOL_Obool),X2159,X2160)
| X2160 != X2159 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_586])])]) ).
fof(i_0_1006,plain,
! [X2148,X2149,X2150] :
( X2150 != X2149
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2148,tc_HOL_Obool),X2150,X2149) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_1007,plain,
! [X2151,X2152,X2153] :
( X2153 != X2152
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2151,tc_HOL_Obool),X2152,X2153) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_1008,plain,
! [X2298] : c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2298,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_1009,plain,
! [X2402] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2402)),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_1010,plain,
! [X2143,X2144] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2144,tc_HOL_Obool),X2143,X2143),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_1011,plain,
! [X1698,X1699] :
( ( c_Finite__Set_Ocard(X1699,X1698) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1698 = c_Orderings_Obot__class_Obot(tc_fun(X1699,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X1699,X1698) )
& ( X1698 != c_Orderings_Obot__class_Obot(tc_fun(X1699,tc_HOL_Obool))
| c_Finite__Set_Ocard(X1699,X1698) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X1699,X1698)
| c_Finite__Set_Ocard(X1699,X1698) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_587])])]) ).
fof(i_0_1012,plain,
! [X2401] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2401,hAPP(c_Nat_OSuc,X2401)),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_1013,plain,
! [X2989] :
( ~ class_Rings_Olinordered__semidom(X2989)
| c_Orderings_Oord__class_Oless(X2989,c_Groups_Ozero__class_Ozero(X2989),c_Groups_Oone__class_Oone(X2989)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_1014,plain,
! [X2987] :
( ~ class_Rings_Olinordered__semidom(X2987)
| c_Orderings_Oord__class_Oless__eq(X2987,c_Groups_Ozero__class_Ozero(X2987),c_Groups_Oone__class_Oone(X2987)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_1015,plain,
! [X3014] :
( ~ class_Rings_Oring__1(X3014)
| c_member(X3014,c_Groups_Oone__class_Oone(X3014),c_Int_Oring__1__class_OInts(X3014)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).
fof(i_0_1016,plain,
! [X3010] :
( ~ class_Rings_Oring__1(X3010)
| c_member(X3010,c_Groups_Ozero__class_Ozero(X3010),c_Int_Oring__1__class_OInts(X3010)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).
fof(i_0_1017,plain,
! [X1658] :
( ~ class_Finite__Set_Ofinite(X1658)
| c_Finite__Set_Ofinite(X1658,c_Orderings_Otop__class_Otop(tc_fun(X1658,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).
fof(i_0_1018,plain,
! [X3203,X3204] :
( ~ hBOOL(hAPP(c_fequal(X3204),X3203))
| X3204 = X3203 ),
inference(variable_rename,[status(thm)],[i_0_588]) ).
fof(i_0_1019,plain,
! [X2823,X2824] :
( ~ class_Rings_Ocomm__semiring__1(X2824)
| c_Groups_Oplus__class_Oplus(X2824,c_Groups_Ozero__class_Ozero(X2824),X2823) = X2823 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_1020,plain,
! [X2694,X2695] :
( ~ class_Groups_Omonoid__add(X2695)
| c_Groups_Oplus__class_Oplus(X2695,c_Groups_Ozero__class_Ozero(X2695),X2694) = X2694 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_1021,plain,
! [X2692,X2693] :
( ~ class_Groups_Ocomm__monoid__add(X2693)
| c_Groups_Oplus__class_Oplus(X2693,c_Groups_Ozero__class_Ozero(X2693),X2692) = X2692 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_1022,plain,
! [X2825,X2826] :
( ~ class_Rings_Ocomm__semiring__1(X2826)
| c_Groups_Oplus__class_Oplus(X2826,X2825,c_Groups_Ozero__class_Ozero(X2826)) = X2825 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_1023,plain,
! [X2688,X2689] :
( ~ class_Groups_Omonoid__add(X2689)
| c_Groups_Oplus__class_Oplus(X2689,X2688,c_Groups_Ozero__class_Ozero(X2689)) = X2688 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_1024,plain,
! [X2686,X2687] :
( ~ class_Groups_Ocomm__monoid__add(X2687)
| c_Groups_Oplus__class_Oplus(X2687,X2686,c_Groups_Ozero__class_Ozero(X2687)) = X2686 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_1025,plain,
! [X2016] : c_Finite__Set_Ocard(X2016,c_Orderings_Obot__class_Obot(tc_fun(X2016,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_card_Oempty]) ).
fof(i_0_1026,plain,
! [X2992] : hAPP(c_Nat_OSuc,X2992) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2992),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1027,plain,
! [X2993] : hAPP(c_Nat_OSuc,X2993) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2993,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1028,plain,
! [X1734,X1735] :
( ~ class_Orderings_Obot(X1735)
| c_Orderings_Oord__class_Oless__eq(X1735,c_Orderings_Obot__class_Obot(X1735),X1734) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])]) ).
fof(i_0_1029,plain,
! [X1973,X1974] :
( ~ class_Orderings_Otop(X1974)
| c_Orderings_Oord__class_Oless__eq(X1974,X1973,c_Orderings_Otop__class_Otop(X1974)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).
fof(i_0_1030,plain,
! [X1975] : c_Finite__Set_Ofinite(X1975,c_Orderings_Obot__class_Obot(tc_fun(X1975,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J]) ).
fof(i_0_1031,plain,
! [X1728] : c_Finite__Set_Ofinite(X1728,c_Orderings_Obot__class_Obot(tc_fun(X1728,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_finite_OemptyI]) ).
fof(i_0_1032,plain,
! [X1815,X1816,X1817] :
( ~ class_Orderings_Opreorder(X1817)
| X1816 != X1815
| c_Orderings_Oord__class_Oless__eq(X1817,X1816,X1815) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_1033,plain,
! [X1726,X1727] :
( ~ class_Orderings_Opreorder(X1727)
| c_Orderings_Oord__class_Oless__eq(X1727,X1726,X1726) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_1034,plain,
! [X2246] :
( X2246 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2246) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_1035,plain,
! [X2656] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2656) = X2656,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_1036,plain,
! [X2655] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2655,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2655,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_1037,plain,
! [X2164,X2165] :
( X2165 != X2164
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2165,X2164) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_1038,plain,
! [X2272] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2272),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_1039,plain,
! [X2031] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2031),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_1040,plain,
! [X2506,X2507,X2508] :
( ( c_SetInterval_Oord__class_OgreaterThan(X2508,X2507) != c_SetInterval_Oord__class_OgreaterThan(X2508,X2506)
| X2507 = X2506
| ~ class_Orderings_Olinorder(X2508) )
& ( X2507 != X2506
| c_SetInterval_Oord__class_OgreaterThan(X2508,X2507) = c_SetInterval_Oord__class_OgreaterThan(X2508,X2506)
| ~ class_Orderings_Olinorder(X2508) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff])])]) ).
fof(i_0_1041,plain,
! [X2161] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2161,X2161),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_1042,plain,
! [X3205,X3206] :
( X3206 != X3205
| hBOOL(hAPP(c_fequal(X3206),X3205)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1043,plain,
! [X3201,X3202] :
( ~ class_Finite__Set_Ofinite(X3202)
| ~ class_Finite__Set_Ofinite(X3201)
| class_Finite__Set_Ofinite(tc_prod(X3202,X3201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).
fof(i_0_1044,plain,
! [X3198,X3199] :
( ~ class_Finite__Set_Ofinite(X3199)
| ~ class_Finite__Set_Ofinite(X3198)
| class_Finite__Set_Ofinite(tc_sum(X3199,X3198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).
fof(i_0_1045,plain,
! [X3188,X3189] :
( ~ class_Finite__Set_Ofinite(X3189)
| ~ class_Finite__Set_Ofinite(X3188)
| class_Finite__Set_Ofinite(tc_fun(X3189,X3188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).
fof(i_0_1046,plain,
! [X2407,X2408] :
( hAPP(c_Nat_OSuc,X2408) != hAPP(c_Nat_OSuc,X2407)
| X2408 = X2407 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1047,plain,
! [X2405,X2406] :
( ( hAPP(c_Nat_OSuc,X2406) != hAPP(c_Nat_OSuc,X2405)
| X2406 = X2405 )
& ( X2406 != X2405
| hAPP(c_Nat_OSuc,X2406) = hAPP(c_Nat_OSuc,X2405) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1048,plain,
! [X3190,X3191] :
( ~ class_Orderings_Oorder(X3191)
| class_Orderings_Oorder(tc_fun(X3190,X3191)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1049,plain,
! [X3194,X3195] :
( ~ class_Orderings_Oord(X3195)
| class_Orderings_Oord(tc_fun(X3194,X3195)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1050,plain,
! [X3196,X3197] :
( ~ class_Orderings_Obot(X3197)
| class_Orderings_Obot(tc_fun(X3196,X3197)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])]) ).
fof(i_0_1051,plain,
! [X3186,X3187] :
( ~ class_Orderings_Opreorder(X3187)
| class_Orderings_Opreorder(tc_fun(X3186,X3187)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1052,plain,
! [X3192,X3193] :
( ~ class_Orderings_Otop(X3193)
| class_Orderings_Otop(tc_fun(X3192,X3193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).
fof(i_0_1053,plain,
! [X1659,X1660] :
( c_Finite__Set_Ofinite(X1660,X1659)
| c_Finite__Set_Ocard(X1660,X1659) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_589])]) ).
fof(i_0_1054,plain,
! [X2462] : hAPP(c_Nat_OSuc,X2462) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1055,plain,
! [X2461] : hAPP(c_Nat_OSuc,X2461) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1056,plain,
! [X2459] : hAPP(c_Nat_OSuc,X2459) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1057,plain,
! [X2464] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2464),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1058,plain,
! [X2463] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2463),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1059,plain,
! [X2460] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2460),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1060,plain,
! [X1652,X1653] :
( ~ class_Finite__Set_Ofinite(X1653)
| c_Finite__Set_Ofinite(X1653,X1652) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
fof(i_0_1061,plain,
! [X1647,X1648] :
( ~ class_Finite__Set_Ofinite(X1648)
| c_Finite__Set_Ofinite(X1648,X1647) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).
fof(i_0_1062,plain,
! [X2404] : hAPP(c_Nat_OSuc,X2404) != X2404,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1063,plain,
! [X2403] : X2403 != hAPP(c_Nat_OSuc,X2403),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1064,plain,
! [X2991] :
( ~ class_Rings_Ozero__neq__one(X2991)
| c_Groups_Ozero__class_Ozero(X2991) != c_Groups_Oone__class_Oone(X2991) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_1065,plain,
! [X2990] :
( ~ class_Rings_Ozero__neq__one(X2990)
| c_Groups_Oone__class_Oone(X2990) != c_Groups_Ozero__class_Ozero(X2990) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_1066,plain,
! [X3200] :
( ~ class_Finite__Set_Ofinite(X3200)
| class_Finite__Set_Ofinite(tc_Option_Ooption(X3200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).
fof(i_0_1067,plain,
! [X2904] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X2904) = X2904,
inference(variable_rename,[status(thm)],[fact_nat__size]) ).
fof(i_0_1068,plain,
~ hBOOL(c_fFalse),
inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).
fof(i_0_1069,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).
cnf(i_0_1070,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X8,X2,X3) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8,X1,X4)
| hAPP(X1,esk33_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,hAPP(X5,esk33_8(X2,X1,X3,X4,X5,X6,X7,X8)))
| X3 != 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_590]),
[final] ).
cnf(i_0_1071,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8,X1,c_SetInterval_Oord__class_OatLeastLessThan(X7,X6,X4)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8,X2,c_SetInterval_Oord__class_OatLeastLessThan(X7,X5,X3))
| hAPP(X1,esk34_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,esk34_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_591]),
[final] ).
cnf(i_0_1072,plain,
( c_member(X1,esk33_8(X2,X3,X4,X5,X6,X7,X1,X8),X5)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8,X2,X4) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8,X3,X5)
| X4 != 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_590]),
[final] ).
cnf(i_0_1073,plain,
( c_Orderings_Oord__class_Oless(X1,esk34_8(X2,X3,X4,X5,X6,X7,X1,X8),X4)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8,X3,c_SetInterval_Oord__class_OatLeastLessThan(X1,X7,X5)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8,X2,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_591]),
[final] ).
cnf(i_0_1074,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,esk34_8(X3,X4,X5,X6,X2,X7,X1,X8))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8,X4,c_SetInterval_Oord__class_OatLeastLessThan(X1,X7,X6)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8,X3,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_591]),
[final] ).
cnf(i_0_1075,plain,
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X4,hAPP(X3,X5)) = hAPP(X3,c_Set_Oimage(X1,X1,X4,X5))
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| hAPP(X4,hAPP(hAPP(X2,esk24_5(X5,X4,X3,X2,X1)),esk25_5(X5,X4,X3,X2,X1))) != hAPP(hAPP(X2,hAPP(X4,esk24_5(X5,X4,X3,X2,X1))),hAPP(X4,esk25_5(X5,X4,X3,X2,X1)))
| ~ c_Finite__Set_Ofinite(X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1076,plain,
( c_Orderings_Oord__class_Oless(X1,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1,X2,X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1,X3,X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(X2,esk31_5(X3,X2,X4,X5,X1)),hAPP(X3,esk31_5(X3,X2,X4,X5,X1)))
| ~ 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_593]),
[final] ).
cnf(i_0_1077,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)
| ~ c_Finite__Set_Ofinite(X2,X7)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X8,X7) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1078,plain,
( hAPP(X6,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)
| ~ c_Finite__Set_Ofinite(X2,X7) ),
inference(split_conjunct,[status(thm)],[i_0_595]),
[final] ).
cnf(i_0_1079,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)
| ~ c_Finite__Set_Ofinite(X2,X7)
| ~ c_member(X2,X8,X7) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1080,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_597]),
[final] ).
cnf(i_0_1081,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_member(X4,X2,c_SetInterval_Oord_OatLeastLessThan(X4,X5,X1,X6,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1082,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_member(X4,X2,c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X5,X6,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1083,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_member(X4,X3,c_SetInterval_Oord_OatLeastLessThan(X4,X1,X5,X2,X6)) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1084,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_member(X4,X3,c_SetInterval_Oord_OgreaterThanAtMost(X4,X5,X1,X2,X6)) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1085,plain,
( X1 = hAPP(X2,esk5_5(X1,X2,X3,X4,X5))
| c_member(X3,X1,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_600]),
[final] ).
cnf(i_0_1086,plain,
( c_member(X1,esk31_5(X2,X3,X4,X1,X5),X4)
| c_Orderings_Oord__class_Oless(X5,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5,X3,X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5,X2,X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ 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_593]),
[final] ).
cnf(i_0_1087,plain,
( X1 = c_Set_Oimage(X2,X3,X4,esk19_5(X5,X4,X2,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oimage(X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1088,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,X4,X5),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X4,c_Set_Oimage(X1,X5,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1089,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk6_4(X3,X2,X4,X1)),hAPP(X3,esk6_4(X3,X2,X4,X1)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1090,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X4,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X5))) = c_Groups_Oplus__class_Oplus(X1,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X4,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X4,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X5))))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1091,plain,
( c_member(X3,X1,c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))
| esk5_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_600]),
[final] ).
cnf(i_0_1092,plain,
( 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_598]),
[final] ).
cnf(i_0_1093,plain,
( 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_599]),
[final] ).
cnf(i_0_1094,plain,
( c_Finite__Set_Ocard(X1,X4) = c_Finite__Set_Ocard(X2,X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4),X5)
| ~ c_Fun_Oinj__on(X2,X1,X6,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X6,X5),X4)
| ~ c_Finite__Set_Ofinite(X1,X4)
| ~ c_Finite__Set_Ofinite(X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1095,plain,
( c_member(X1,hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5),X6)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_member(X2,X5,c_Set_Oimage(X1,X2,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X6) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1096,plain,
( hAPP(X3,hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_member(X2,X5,c_Set_Oimage(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1097,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4),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_607]),
[final] ).
cnf(i_0_1098,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(X1,c_Set_Oimage(X2,X1,X3,X4)),c_Finite__Set_Ocard(X2,X4))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_608]),
[final] ).
cnf(i_0_1099,plain,
( c_Set_Oimage(X2,X1,esk8_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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1100,plain,
( X1 = hAPP(X2,esk4_4(X1,X2,X3,X4))
| ~ c_member(X3,X1,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_600]),
[final] ).
cnf(i_0_1101,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk9_4(X3,X1,X2,X4),X4),X3)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X1,X2,X5,X3) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1102,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X3)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3,X4))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X4))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_610]),
[final] ).
cnf(i_0_1103,plain,
( X3 = esk4_4(X1,X2,X4,X5)
| X1 != hAPP(X2,X3)
| ~ c_member(X4,X1,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_600]),
[final] ).
cnf(i_0_1104,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk7_4(X3,X1,X4,X2),X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2,X4),c_Finite__Set_Ocard(X1,X3))
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1105,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2),c_Set_Oimage(X1,X4,X5,X3))
| ~ 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_607]),
[final] ).
cnf(i_0_1106,plain,
( c_Set_Oimage(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),c_Set_Oimage(X1,X2,X3,X4)) = X4
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_1107,plain,
( c_Fun_Oinj__on(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),c_Set_Oimage(X1,X2,X3,X4))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1108,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X5),c_Set_Oimage(X1,X2,X3,X4))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_614]),
[final] ).
cnf(i_0_1109,plain,
( c_Set_Oimage(X1,X1,X3,X2) = X2
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X1,X1,X3,X2),X2)
| ~ c_Fun_Oinj__on(X1,X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1110,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(X1,esk32_4(X2,X3,X1,X4)))
| 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_616]),
[final] ).
cnf(i_0_1111,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4),c_Finite__Set_Ocard(X2,X5))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4),X5)
| ~ c_Finite__Set_Ofinite(X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1112,plain,
( c_member(X4,X3,X5)
| ~ c_member(X1,hAPP(X2,X3),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_617]),
[final] ).
cnf(i_0_1113,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4),c_Finite__Set_Ocard(X2,X5))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4),X5)
| ~ c_Finite__Set_Ofinite(X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1114,plain,
( c_member(X1,esk18_4(X2,X3,X1,X4),X2)
| ~ c_member(X5,X4,c_Set_Oimage(X1,X5,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1115,plain,
( X1 = hAPP(X2,esk18_4(X3,X2,X4,X1))
| ~ c_member(X5,X1,c_Set_Oimage(X4,X5,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1116,plain,
( c_Finite__Set_Ocard(X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(X1,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_member(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1117,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X4,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,hAPP(X4,X2),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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1118,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,hAPP(X4,X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3)))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_622]),
[final] ).
cnf(i_0_1119,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| 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_Oplus__class_Oplus(X3,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_623]),
[final] ).
cnf(i_0_1120,plain,
( hAPP(X1,esk2_4(X2,X1,X3,X4)) = hAPP(X1,esk3_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1121,plain,
( X4 = X5
| c_Set_Oimage(X1,X2,X3,X4) != 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_625]),
[final] ).
cnf(i_0_1122,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) = c_Groups_Oplus__class_Oplus(X3,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,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_626]),
[final] ).
cnf(i_0_1123,plain,
( 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,esk30_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_member(X3,X4,X2)
| hAPP(X1,X4) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1124,plain,
( c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,X4))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_628]),
[final] ).
cnf(i_0_1125,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2),c_Set_Oimage(X1,X4,X5,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_629]),
[final] ).
cnf(i_0_1126,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(X1,esk40_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_member(X3,X4,X2)
| hAPP(X1,X4) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1127,hypothesis,
( v_thesis____
| ~ c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
| c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_631]),
[final] ).
cnf(i_0_1128,plain,
( c_Fun_Oinj__on(X1,X1,X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X1,X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_632]),
[final] ).
cnf(i_0_1129,plain,
( c_Fun_Oinj__on(X1,X2,esk9_4(X3,X2,X1,X4),X4)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Set_Oimage(X2,X1,X5,X3) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1130,plain,
( c_member(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3))
| ~ 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_617]),
[final] ).
cnf(i_0_1131,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3,c_Set_Oimage(X1,X3,X4,X2)),c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_633]),
[final] ).
cnf(i_0_1132,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_634]),
[final] ).
cnf(i_0_1133,plain,
( c_Fun_Oinj__on(X1,X3,X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X3,c_Set_Oimage(X1,X3,X4,X2)) != c_Finite__Set_Ocard(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_635]),
[final] ).
cnf(i_0_1134,plain,
( c_Fun_Oinj__on(X2,X1,X3,X4)
| c_Finite__Set_Ocard(X1,c_Set_Oimage(X2,X1,X3,X4)) != c_Finite__Set_Ocard(X2,X4)
| ~ c_Finite__Set_Ofinite(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_636]),
[final] ).
cnf(i_0_1135,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X4,c_Set_Oimage(X1,X5,X6,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X4 != c_Set_Oimage(X1,X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1136,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk2_4(X1,X2,X3,X4) != esk3_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1137,plain,
( c_member(X2,X4,X3)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1,X5,c_Set_Oinsert(X2,X4,X3)) = c_Groups_Oplus__class_Oplus(X1,hAPP(X5,X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1,X5,X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1138,plain,
( c_member(X2,X4,X3)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1,X5,c_Set_Oinsert(X2,X4,X3)) = c_Groups_Oplus__class_Oplus(X1,hAPP(X5,X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1,X5,X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_638]),
[final] ).
cnf(i_0_1139,plain,
( hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_member(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_639]),
[final] ).
cnf(i_0_1140,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
| ~ c_member(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_640]),
[final] ).
cnf(i_0_1141,plain,
( c_member(X1,esk30_4(X2,X3,X1,X4),X3)
| 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))
| ~ c_member(X1,X4,X3)
| hAPP(X2,X4) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1142,plain,
( X1 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Finite__Set_Ocard(tc_Nat_Onat,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Finite__Set_Ocard(tc_Nat_Onat,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1143,plain,
( c_member(X1,esk32_4(X2,X3,X4,X1),X3)
| 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_616]),
[final] ).
cnf(i_0_1144,plain,
( c_Fun_Oinj__on(X1,X2,esk7_4(X3,X2,X4,X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4),c_Finite__Set_Ocard(X2,X3))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1145,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_member(X4,X2,c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X5,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1146,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_member(X4,X2,c_SetInterval_Oord_OatLeastAtMost(X4,X1,X5,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1147,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_member(X4,X3,c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X2,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1148,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_member(X4,X3,c_SetInterval_Oord_OatLeastAtMost(X4,X1,X2,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1149,plain,
( c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X4,c_Set_Oimage(X1,X3,X5,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_644]),
[final] ).
cnf(i_0_1150,plain,
( c_Finite__Set_Ocard(X2,c_Set_Oimage(X1,X2,X3,X4)) = c_Finite__Set_Ocard(X1,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_636]),
[final] ).
cnf(i_0_1151,plain,
( c_member(X1,esk40_4(X2,X3,X1,X4),X3)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat,X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_member(X1,X4,X3)
| hAPP(X2,X4) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1152,plain,
c_Set_Oimage(X1,X2,X3,c_Set_Oinsert(X1,X4,X5)) = c_Set_Oinsert(X2,hAPP(X3,X4),c_Set_Oimage(X1,X2,X3,X5)),
inference(split_conjunct,[status(thm)],[i_0_645]),
[final] ).
cnf(i_0_1153,plain,
( c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| 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_646]),
[final] ).
cnf(i_0_1154,plain,
( c_Finite__Set_Ocard(X2,c_Set_Oimage(X1,X2,X3,X4)) = c_Finite__Set_Ocard(X1,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1155,plain,
( c_Set_Oinsert(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3)) = c_Set_Oimage(X1,X4,X5,X3)
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1156,plain,
( 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))
| ~ 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_649]),
[final] ).
cnf(i_0_1157,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1158,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(tc_sum(X3,X1),c_Sum__Type_OPlus(X3,X1,X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1159,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(tc_sum(X1,X2),c_Sum__Type_OPlus(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1160,plain,
( c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(tc_sum(X1,X2),c_Sum__Type_OPlus(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1161,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_653]),
[final] ).
cnf(i_0_1162,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,X5,c_Set_Oinsert(X4,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X2,c_Set_Oinsert(X4,X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_653]),
[final] ).
cnf(i_0_1163,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X5,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_653]),
[final] ).
cnf(i_0_1164,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X2,c_Set_Oinsert(X4,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_653]),
[final] ).
cnf(i_0_1165,plain,
( 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 != esk30_4(X2,X3,X4,X1)
| ~ c_member(X4,X1,X3)
| hAPP(X2,X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Finite__Set_Ofinite(X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1166,plain,
( 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_642]),
[final] ).
cnf(i_0_1167,plain,
( 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_643]),
[final] ).
cnf(i_0_1168,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X2,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_654]),
[final] ).
cnf(i_0_1169,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_member(X1,X2,c_Int_Oring__1__class_OInts(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_655]),
[final] ).
cnf(i_0_1170,plain,
( c_member(X1,esk3_4(X2,X3,X4,X1),X2)
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1171,plain,
( c_member(X1,esk2_4(X2,X3,X4,X1),X2)
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1172,plain,
( 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)) = 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_656]),
[final] ).
cnf(i_0_1173,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat,X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != esk40_4(X2,X3,X4,X1)
| ~ c_member(X4,X1,X3)
| hAPP(X2,X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1174,plain,
( c_Fun_Oinj__on(X1,X2,X3,X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1175,plain,
( c_Finite__Set_Ocard(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_658]),
[final] ).
cnf(i_0_1176,plain,
( c_Finite__Set_Ocard(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_659]),
[final] ).
cnf(i_0_1177,plain,
c_member(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_660]),
[final] ).
cnf(i_0_1178,plain,
( c_member(X4,X1,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_661]),
[final] ).
cnf(i_0_1179,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ 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_662]),
[final] ).
cnf(i_0_1180,plain,
( c_member(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3))
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_663]),
[final] ).
cnf(i_0_1181,plain,
( c_member(X6,X1,c_Set_Oimage(X4,X6,X2,X5))
| X1 != hAPP(X2,X3)
| ~ c_member(X4,X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1182,plain,
( c_member(X6,X4,c_Set_Oimage(X1,X6,X5,X3))
| ~ c_member(X1,X2,X3)
| X4 != hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1183,plain,
( c_member(X6,X4,c_Set_Oimage(X1,X6,X5,X3))
| ~ c_member(X1,X2,X3)
| X4 != hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_665]),
[final] ).
cnf(i_0_1184,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X5)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_662]),
[final] ).
cnf(i_0_1185,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_662]),
[final] ).
cnf(i_0_1186,plain,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ c_member(X4,X3,X5)
| ~ c_member(X4,X2,X5)
| ~ c_Fun_Oinj__on(X4,X6,X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_666]),
[final] ).
cnf(i_0_1187,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(X3,X5) != hAPP(X3,X6)
| ~ c_member(X1,X5,X4)
| ~ c_member(X1,X6,X4) ),
inference(split_conjunct,[status(thm)],[i_0_667]),
[final] ).
cnf(i_0_1188,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_member(X1,X5,X4)
| ~ c_member(X1,X6,X4)
| hAPP(X3,X5) != hAPP(X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1189,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_member(X1,X5,X4)
| ~ c_member(X1,X6,X4)
| hAPP(X3,X5) != hAPP(X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1190,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ 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_662]),
[final] ).
cnf(i_0_1191,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ 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_669]),
[final] ).
cnf(i_0_1192,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ 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_662]),
[final] ).
cnf(i_0_1193,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ 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_669]),
[final] ).
cnf(i_0_1194,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_member(X1,X2,c_Int_Oring__1__class_OInts(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_655]),
[final] ).
cnf(i_0_1195,plain,
( c_member(X1,esk29_3(X2,X3,X1),X3)
| 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))
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1196,plain,
( esk29_3(X4,X3,X1) = X2
| hAPP(X4,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_member(X1,X2,X3)
| 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))
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1197,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X2 = c_Set_Oinsert(X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_670]),
[final] ).
cnf(i_0_1198,plain,
( c_Finite__Set_Ofinite(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_671]),
[final] ).
cnf(i_0_1199,plain,
( c_Finite__Set_Ofinite(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1200,plain,
( c_member(X1,esk39_3(X2,X3,X1),X3)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat,X2,X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1201,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X2),c_SetInterval_Oord__class_OatLeastLessThan(X1,X5,X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_672]),
[final] ).
cnf(i_0_1202,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X5))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_672]),
[final] ).
cnf(i_0_1203,plain,
( esk39_3(X4,X3,X1) = X2
| hAPP(X4,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_member(X1,X2,X3)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat,X4,X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1204,plain,
( hAPP(X1,esk29_3(X1,X2,X3)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| 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))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1205,plain,
( c_Finite__Set_Ofinite(X1,X2)
| 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_659]),
[final] ).
cnf(i_0_1206,plain,
( c_Finite__Set_Ofinite(X1,X2)
| 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_659]),
[final] ).
cnf(i_0_1207,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_673]),
[final] ).
cnf(i_0_1208,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_674]),
[final] ).
cnf(i_0_1209,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_674]),
[final] ).
cnf(i_0_1210,plain,
( c_Set_Oinsert(X5,X1,c_Set_Oinsert(X5,X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Set_Oinsert(X5,X4,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_653]),
[final] ).
cnf(i_0_1211,plain,
( hAPP(X1,esk39_3(X1,X2,X3)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1212,plain,
( c_Finite__Set_Ofinite(X3,c_Set_Oimage(X1,X3,X4,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_675]),
[final] ).
cnf(i_0_1213,plain,
( 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)
| ~ 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_623]),
[final] ).
cnf(i_0_1214,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ 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_662]),
[final] ).
cnf(i_0_1215,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_676]),
[final] ).
cnf(i_0_1216,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_677]),
[final] ).
cnf(i_0_1217,plain,
( hAPP(X2,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_member(X1,X4,X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_678]),
[final] ).
cnf(i_0_1218,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) = c_Groups_Ozero__class_Ozero(X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_626]),
[final] ).
cnf(i_0_1219,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_1220,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_680]),
[final] ).
cnf(i_0_1221,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_681]),
[final] ).
cnf(i_0_1222,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_682]),
[final] ).
cnf(i_0_1223,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_683]),
[final] ).
cnf(i_0_1224,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_1225,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_1226,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_1227,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1228,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(X1,esk28_3(X1,X2,X3)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_678]),
[final] ).
cnf(i_0_1229,plain,
( ~ c_member(X1,esk43_3(X2,X3,X1),esk44_3(X2,X3,X1))
| c_Finite__Set_Ocard(X1,X3) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_1230,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_1231,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1232,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_Set_Oimage(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_1233,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| 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_691]),
[final] ).
cnf(i_0_1234,plain,
( 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))
| c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ 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_692]),
[final] ).
cnf(i_0_1235,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_693]),
[final] ).
cnf(i_0_1236,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_694]),
[final] ).
cnf(i_0_1237,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_695]),
[final] ).
cnf(i_0_1238,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_696]),
[final] ).
cnf(i_0_1239,plain,
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_697]),
[final] ).
cnf(i_0_1240,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2)) = 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_698]),
[final] ).
cnf(i_0_1241,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| 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))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_662]),
[final] ).
cnf(i_0_1242,plain,
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk41_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_699]),
[final] ).
cnf(i_0_1243,plain,
( c_member(X1,esk28_3(X2,X3,X1),X3)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_678]),
[final] ).
cnf(i_0_1244,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_700]),
[final] ).
cnf(i_0_1245,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_1246,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_702]),
[final] ).
cnf(i_0_1247,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4)
| c_member(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_703]),
[final] ).
cnf(i_0_1248,plain,
( X2 = X3
| ~ c_member(X1,X2,c_Set_Oinsert(X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_704]),
[final] ).
cnf(i_0_1249,plain,
( X2 = X3
| ~ c_member(X1,X2,c_Set_Oinsert(X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_1250,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk37_2(X1,X2)))
| ~ 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_706]),
[final] ).
cnf(i_0_1251,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk20_2(X1,X2)))
| ~ c_member(tc_Nat_Onat,X3,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_707]),
[final] ).
cnf(i_0_1252,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_708]),
[final] ).
cnf(i_0_1253,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_674]),
[final] ).
cnf(i_0_1254,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2),c_Set_Oinsert(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1255,plain,
( c_Finite__Set_Ofinite(tc_prod(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_710]),
[final] ).
cnf(i_0_1256,plain,
( c_Finite__Set_Ofinite(tc_sum(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_1257,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X4),X3)
| ~ c_member(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_1258,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)
| ~ c_Finite__Set_Ofinite(X1,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_713]),
[final] ).
cnf(i_0_1259,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_714]),
[final] ).
cnf(i_0_1260,plain,
( hBOOL(hAPP(X1,esk36_2(X1,X2)))
| ~ 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_715]),
[final] ).
cnf(i_0_1261,plain,
( hBOOL(hAPP(X1,esk11_2(X1,X2)))
| ~ c_member(tc_Nat_Onat,X3,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_716]),
[final] ).
cnf(i_0_1262,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk11_2(X1,X2),X2)
| ~ c_member(tc_Nat_Onat,X3,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_716]),
[final] ).
cnf(i_0_1263,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk36_2(X1,X2),X2)
| ~ 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_715]),
[final] ).
cnf(i_0_1264,plain,
( ~ class_Int_Oring__char__0(X1)
| ~ c_member(X1,X2,c_Int_Oring__1__class_OInts(X1))
| c_Groups_Oplus__class_Oplus(X1,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_717]),
[final] ).
cnf(i_0_1265,plain,
( c_member(X1,X5,X4)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X3,c_Set_Oinsert(X1,X5,X4)) = hAPP(hAPP(X2,X5),hAPP(X3,X4))
| ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_718]),
[final] ).
cnf(i_0_1266,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) = c_Set_Oinsert(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_719]),
[final] ).
cnf(i_0_1267,plain,
( c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ 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_711]),
[final] ).
cnf(i_0_1268,plain,
( c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ 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_711]),
[final] ).
cnf(i_0_1269,plain,
( c_Finite__Set_Ofinite(X2,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
| ~ 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_720]),
[final] ).
cnf(i_0_1270,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_1271,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_721]),
[final] ).
cnf(i_0_1272,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_722]),
[final] ).
cnf(i_0_1273,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_723]),
[final] ).
cnf(i_0_1274,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_724]),
[final] ).
cnf(i_0_1275,plain,
( c_member(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Oring__1__class_OInts(X1))
| ~ class_Rings_Oring__1(X1)
| ~ c_member(X1,X2,c_Int_Oring__1__class_OInts(X1))
| ~ c_member(X1,X3,c_Int_Oring__1__class_OInts(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_725]),
[final] ).
cnf(i_0_1276,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_726]),
[final] ).
cnf(i_0_1277,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_727]),
[final] ).
cnf(i_0_1278,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_728]),
[final] ).
cnf(i_0_1279,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_729]),
[final] ).
cnf(i_0_1280,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk20_2(X1,X2),X2)
| hBOOL(hAPP(X1,X3))
| ~ c_member(tc_Nat_Onat,X3,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_707]),
[final] ).
cnf(i_0_1281,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk37_2(X1,X2),X2)
| hBOOL(hAPP(X1,X3))
| ~ 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_706]),
[final] ).
cnf(i_0_1282,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_730]),
[final] ).
cnf(i_0_1283,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_731]),
[final] ).
cnf(i_0_1284,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_1285,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_732]),
[final] ).
cnf(i_0_1286,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_681]),
[final] ).
cnf(i_0_1287,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_733]),
[final] ).
cnf(i_0_1288,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ 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_683]),
[final] ).
cnf(i_0_1289,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_734]),
[final] ).
cnf(i_0_1290,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ 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_685]),
[final] ).
cnf(i_0_1291,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X4,X3))
| c_member(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_703]),
[final] ).
cnf(i_0_1292,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) != c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X5)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X5)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1293,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) != c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X5,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1294,plain,
( X2 = X4
| ~ class_Orderings_Olinorder(X1)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1295,plain,
( X3 = X5
| ~ class_Orderings_Olinorder(X1)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_737]),
[final] ).
cnf(i_0_1296,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| 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_669]),
[final] ).
cnf(i_0_1297,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_738]),
[final] ).
cnf(i_0_1298,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_739]),
[final] ).
cnf(i_0_1299,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_740]),
[final] ).
cnf(i_0_1300,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_1301,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_742]),
[final] ).
cnf(i_0_1302,plain,
( c_member(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_1303,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_743]),
[final] ).
cnf(i_0_1304,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_1305,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_744]),
[final] ).
cnf(i_0_1306,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1307,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X3,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_745]),
[final] ).
cnf(i_0_1308,plain,
( X2 = X3
| c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) != c_Set_Oinsert(X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_746]),
[final] ).
cnf(i_0_1309,plain,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ c_member(X1,X2,c_SetInterval_Oord_OlessThan(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_747]),
[final] ).
cnf(i_0_1310,plain,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ c_member(X1,X2,c_SetInterval_Oord_OatMost(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_748]),
[final] ).
cnf(i_0_1311,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ c_member(X1,X2,c_SetInterval_Oord_OgreaterThan(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_749]),
[final] ).
cnf(i_0_1312,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ c_member(X1,X2,c_SetInterval_Oord_OatLeast(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_750]),
[final] ).
cnf(i_0_1313,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_751]),
[final] ).
cnf(i_0_1314,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_752]),
[final] ).
cnf(i_0_1315,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,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_753]),
[final] ).
cnf(i_0_1316,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,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_754]),
[final] ).
cnf(i_0_1317,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,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_755]),
[final] ).
cnf(i_0_1318,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_756]),
[final] ).
cnf(i_0_1319,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_757]),
[final] ).
cnf(i_0_1320,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_758]),
[final] ).
cnf(i_0_1321,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_759]),
[final] ).
cnf(i_0_1322,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_1323,plain,
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_761]),
[final] ).
cnf(i_0_1324,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X3,c_Set_Oinsert(X1,X5,X4)) = hAPP(hAPP(X2,X5),hAPP(X3,X4))
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_1325,plain,
c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,X4)) = c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_763]),
[final] ).
cnf(i_0_1326,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_764]),
[final] ).
cnf(i_0_1327,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_765]),
[final] ).
cnf(i_0_1328,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_766]),
[final] ).
cnf(i_0_1329,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_767]),
[final] ).
cnf(i_0_1330,plain,
( c_member(tc_Nat_Onat,esk35_2(X1,X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_1331,plain,
( c_member(tc_Nat_Onat,esk10_2(X1,X2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_716]),
[final] ).
cnf(i_0_1332,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = 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_690]),
[final] ).
cnf(i_0_1333,plain,
( 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_691]),
[final] ).
cnf(i_0_1334,plain,
( c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) = c_Set_Oinsert(tc_Nat_Onat,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_768]),
[final] ).
cnf(i_0_1335,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_769]),
[final] ).
cnf(i_0_1336,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_770]),
[final] ).
cnf(i_0_1337,plain,
( X3 = X2
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_771]),
[final] ).
cnf(i_0_1338,plain,
( X2 = X3
| c_member(X1,X2,X4)
| ~ c_member(X1,X2,c_Set_Oinsert(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_772]),
[final] ).
cnf(i_0_1339,plain,
( X2 = X3
| c_member(X1,X2,X4)
| ~ c_member(X1,X2,c_Set_Oinsert(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_773]),
[final] ).
cnf(i_0_1340,plain,
( X1 = c_Set_Oinsert(X2,esk43_3(X3,X1,X2),esk44_3(X3,X1,X2))
| c_Finite__Set_Ocard(X2,X1) != hAPP(c_Nat_OSuc,X3) ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_1341,plain,
( 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_774]),
[final] ).
cnf(i_0_1342,plain,
( 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_775]),
[final] ).
cnf(i_0_1343,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_776]),
[final] ).
cnf(i_0_1344,plain,
c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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_1345,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_777]),
[final] ).
cnf(i_0_1346,plain,
( c_member(tc_Nat_Onat,esk38_2(X1,X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))
| hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_706]),
[final] ).
cnf(i_0_1347,plain,
( c_member(tc_Nat_Onat,esk21_2(X1,X2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))
| hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_707]),
[final] ).
cnf(i_0_1348,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_778]),
[final] ).
cnf(i_0_1349,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_779]),
[final] ).
cnf(i_0_1350,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_779]),
[final] ).
cnf(i_0_1351,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1352,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_781]),
[final] ).
cnf(i_0_1353,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_782]),
[final] ).
cnf(i_0_1354,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ 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_783]),
[final] ).
cnf(i_0_1355,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X3,X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ 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_783]),
[final] ).
cnf(i_0_1356,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X4,X3)
| c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_784]),
[final] ).
cnf(i_0_1357,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X4,X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_708]),
[final] ).
cnf(i_0_1358,plain,
( c_member(X4,X2,c_SetInterval_Oord_OlessThan(X4,X1,X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_747]),
[final] ).
cnf(i_0_1359,plain,
( c_member(X4,X2,c_SetInterval_Oord_OatMost(X4,X1,X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_748]),
[final] ).
cnf(i_0_1360,plain,
( c_member(X4,X3,c_SetInterval_Oord_OgreaterThan(X4,X1,X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_749]),
[final] ).
cnf(i_0_1361,plain,
( c_member(X4,X3,c_SetInterval_Oord_OatLeast(X4,X1,X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_750]),
[final] ).
cnf(i_0_1362,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_785]),
[final] ).
cnf(i_0_1363,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_786]),
[final] ).
cnf(i_0_1364,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1365,plain,
( X3 = X4
| c_member(X1,X2,X4)
| c_member(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_788]),
[final] ).
cnf(i_0_1366,plain,
( c_member(X1,X3,X2)
| c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X3,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_789]),
[final] ).
cnf(i_0_1367,plain,
( hAPP(hAPP(X2,X5),hAPP(X3,X4)) = hAPP(X3,X4)
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X4)
| ~ c_member(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_790]),
[final] ).
cnf(i_0_1368,plain,
( 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)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ 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_783]),
[final] ).
cnf(i_0_1369,plain,
( c_Finite__Set_Ofinite(X2,X3)
| 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_791]),
[final] ).
cnf(i_0_1370,plain,
( c_Finite__Set_Ofinite(X2,X3)
| 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_792]),
[final] ).
cnf(i_0_1371,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ 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_753]),
[final] ).
cnf(i_0_1372,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ 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_754]),
[final] ).
cnf(i_0_1373,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ 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_755]),
[final] ).
cnf(i_0_1374,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ 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_751]),
[final] ).
cnf(i_0_1375,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ 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_752]),
[final] ).
cnf(i_0_1376,plain,
( c_member(X3,X1,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_705]),
[final] ).
cnf(i_0_1377,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X1,X2),c_SetInterval_Oord__class_OgreaterThan(X1,X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_793]),
[final] ).
cnf(i_0_1378,plain,
( c_member(X1,X2,X4)
| ~ c_member(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_794]),
[final] ).
cnf(i_0_1379,plain,
( c_member(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_795]),
[final] ).
cnf(i_0_1380,plain,
( c_member(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_796]),
[final] ).
cnf(i_0_1381,plain,
( c_member(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_797]),
[final] ).
cnf(i_0_1382,plain,
( c_member(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_1383,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X2) != 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_799]),
[final] ).
cnf(i_0_1384,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) != 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_799]),
[final] ).
cnf(i_0_1385,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X4,X3)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_784]),
[final] ).
cnf(i_0_1386,plain,
( X2 = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_800]),
[final] ).
cnf(i_0_1387,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk41_2(X2,X3))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_699]),
[final] ).
cnf(i_0_1388,plain,
( X2 = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk27_2(X2,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_801]),
[final] ).
cnf(i_0_1389,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_802]),
[final] ).
cnf(i_0_1390,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_803]),
[final] ).
cnf(i_0_1391,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_730]),
[final] ).
cnf(i_0_1392,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_730]),
[final] ).
cnf(i_0_1393,plain,
( c_member(X1,X2,c_Set_Oinsert(X1,X4,X3))
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_804]),
[final] ).
cnf(i_0_1394,plain,
( c_member(X1,X2,c_Set_Oinsert(X1,X4,X3))
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_772]),
[final] ).
cnf(i_0_1395,plain,
( c_member(X1,X2,c_Set_Oinsert(X1,X4,X3))
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_805]),
[final] ).
cnf(i_0_1396,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_708]),
[final] ).
cnf(i_0_1397,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_806]),
[final] ).
cnf(i_0_1398,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(split_conjunct,[status(thm)],[i_0_807]),
[final] ).
cnf(i_0_1399,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1400,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_809]),
[final] ).
cnf(i_0_1401,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_810]),
[final] ).
cnf(i_0_1402,plain,
( c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X2,X3)) = c_Finite__Set_Ocard(X1,X3)
| ~ c_member(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_811]),
[final] ).
cnf(i_0_1403,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk21_2(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_707]),
[final] ).
cnf(i_0_1404,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk38_2(X1,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_706]),
[final] ).
cnf(i_0_1405,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_812]),
[final] ).
cnf(i_0_1406,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_813]),
[final] ).
cnf(i_0_1407,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1408,plain,
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(X3,X5),hAPP(X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1409,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_815]),
[final] ).
cnf(i_0_1410,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_816]),
[final] ).
cnf(i_0_1411,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_817]),
[final] ).
cnf(i_0_1412,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_818]),
[final] ).
cnf(i_0_1413,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_819]),
[final] ).
cnf(i_0_1414,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_820]),
[final] ).
cnf(i_0_1415,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_821]),
[final] ).
cnf(i_0_1416,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_822]),
[final] ).
cnf(i_0_1417,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 != hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_801]),
[final] ).
cnf(i_0_1418,plain,
( c_member(X2,X4,X1)
| c_Finite__Set_Ocard(X2,X3) = hAPP(c_Nat_OSuc,X5)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X3 != c_Set_Oinsert(X2,X4,X1)
| c_Finite__Set_Ocard(X2,X1) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_1419,plain,
( c_member(X1,X2,X3)
| c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X2,X3)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X1,X3))
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_811]),
[final] ).
cnf(i_0_1420,plain,
( c_member(X1,X3,X2)
| c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,X3,X2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_823]),
[final] ).
cnf(i_0_1421,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_824]),
[final] ).
cnf(i_0_1422,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_825]),
[final] ).
cnf(i_0_1423,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_826]),
[final] ).
cnf(i_0_1424,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_827]),
[final] ).
cnf(i_0_1425,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_1426,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_1427,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_830]),
[final] ).
cnf(i_0_1428,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1429,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ 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_832]),
[final] ).
cnf(i_0_1430,plain,
c_Set_Othe__elem(X1,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2,
inference(split_conjunct,[status(thm)],[i_0_833]),
[final] ).
cnf(i_0_1431,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X1,X3),c_SetInterval_Oord__class_OgreaterThan(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_793]),
[final] ).
cnf(i_0_1432,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_834]),
[final] ).
cnf(i_0_1433,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_835]),
[final] ).
cnf(i_0_1434,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_836]),
[final] ).
cnf(i_0_1435,plain,
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_837]),
[final] ).
cnf(i_0_1436,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_838]),
[final] ).
cnf(i_0_1437,plain,
( c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ 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_839]),
[final] ).
cnf(i_0_1438,plain,
c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X2,X3)) = c_Set_Oinsert(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_840]),
[final] ).
cnf(i_0_1439,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_784]),
[final] ).
cnf(i_0_1440,plain,
( hBOOL(hAPP(X1,esk35_2(X1,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_1441,plain,
( hBOOL(hAPP(X1,esk10_2(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_716]),
[final] ).
cnf(i_0_1442,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ 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_841]),
[final] ).
cnf(i_0_1443,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ 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_842]),
[final] ).
cnf(i_0_1444,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ 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_843]),
[final] ).
cnf(i_0_1445,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_844]),
[final] ).
cnf(i_0_1446,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_845]),
[final] ).
cnf(i_0_1447,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_846]),
[final] ).
cnf(i_0_1448,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_847]),
[final] ).
cnf(i_0_1449,plain,
~ 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_848]),
[final] ).
cnf(i_0_1450,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_849]),
[final] ).
cnf(i_0_1451,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(X1,X2),X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_850]),
[final] ).
cnf(i_0_1452,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_851]),
[final] ).
cnf(i_0_1453,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1454,plain,
( c_Finite__Set_Ofinite(tc_Option_Ooption(X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_839]),
[final] ).
cnf(i_0_1455,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ c_member(X1,X2,c_Int_Oring__1__class_OInts(X1))
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_853]),
[final] ).
cnf(i_0_1456,plain,
( hBOOL(hAPP(X3,X4))
| ~ 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_854]),
[final] ).
cnf(i_0_1457,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_855]),
[final] ).
cnf(i_0_1458,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_856]),
[final] ).
cnf(i_0_1459,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_851]),
[final] ).
cnf(i_0_1460,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1461,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),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_857]),
[final] ).
cnf(i_0_1462,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_member(X3,X4,X5)
| c_Finite__Set_Ocard(X3,X2) = hAPP(c_Nat_OSuc,X1)
| X2 != c_Set_Oinsert(X3,X4,X5)
| c_Finite__Set_Ocard(X3,X5) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_1463,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_858]),
[final] ).
cnf(i_0_1464,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_859]),
[final] ).
cnf(i_0_1465,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X1),X2))
| X2 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_860]),
[final] ).
cnf(i_0_1466,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_member(X1,X2,c_SetInterval_Oord__class_OgreaterThan(X1,X3))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_861]),
[final] ).
cnf(i_0_1467,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = hAPP(c_Nat_OSuc,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_862]),
[final] ).
cnf(i_0_1468,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = hAPP(c_Nat_OSuc,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_863]),
[final] ).
cnf(i_0_1469,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(split_conjunct,[status(thm)],[i_0_864]),
[final] ).
cnf(i_0_1470,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_865]),
[final] ).
cnf(i_0_1471,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_842]),
[final] ).
cnf(i_0_1472,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_866]),
[final] ).
cnf(i_0_1473,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_843]),
[final] ).
cnf(i_0_1474,plain,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_867]),
[final] ).
cnf(i_0_1475,plain,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_868]),
[final] ).
cnf(i_0_1476,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_869]),
[final] ).
cnf(i_0_1477,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_870]),
[final] ).
cnf(i_0_1478,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X3))
| X1 != hAPP(c_Nat_OSuc,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_850]),
[final] ).
cnf(i_0_1479,plain,
( c_Orderings_Oord__class_Oless(X1,X2,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_871]),
[final] ).
cnf(i_0_1480,plain,
( X2 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_872]),
[final] ).
cnf(i_0_1481,plain,
( X2 = X4
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X4,X3)
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_873]),
[final] ).
cnf(i_0_1482,plain,
( X3 = X4
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_874]),
[final] ).
cnf(i_0_1483,plain,
( X3 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_875]),
[final] ).
cnf(i_0_1484,plain,
( X3 = X4
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_876]),
[final] ).
cnf(i_0_1485,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_877]),
[final] ).
cnf(i_0_1486,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_878]),
[final] ).
cnf(i_0_1487,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_879]),
[final] ).
cnf(i_0_1488,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_880]),
[final] ).
cnf(i_0_1489,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_881]),
[final] ).
cnf(i_0_1490,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_882]),
[final] ).
cnf(i_0_1491,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_883]),
[final] ).
cnf(i_0_1492,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_884]),
[final] ).
cnf(i_0_1493,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_885]),
[final] ).
cnf(i_0_1494,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_849]),
[final] ).
cnf(i_0_1495,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_886]),
[final] ).
cnf(i_0_1496,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_887]),
[final] ).
cnf(i_0_1497,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_888]),
[final] ).
cnf(i_0_1498,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1499,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X4,X1,X2) = 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_799]),
[final] ).
cnf(i_0_1500,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1501,plain,
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1502,plain,
c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)) = 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_892]),
[final] ).
cnf(i_0_1503,plain,
( c_member(X1,X3,c_SetInterval_Oord__class_OgreaterThan(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_861]),
[final] ).
cnf(i_0_1504,plain,
( 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_832]),
[final] ).
cnf(i_0_1505,plain,
( hAPP(c_Nat_OSuc,X1) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_893]),
[final] ).
cnf(i_0_1506,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_894]),
[final] ).
cnf(i_0_1507,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_895]),
[final] ).
cnf(i_0_1508,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_896]),
[final] ).
cnf(i_0_1509,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_897]),
[final] ).
cnf(i_0_1510,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_898]),
[final] ).
cnf(i_0_1511,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_899]),
[final] ).
cnf(i_0_1512,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_900]),
[final] ).
cnf(i_0_1513,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = 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_901]),
[final] ).
cnf(i_0_1514,plain,
( c_Groups_Oplus__class_Oplus(X2,X1,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ c_member(X2,X1,c_Int_Oring__1__class_OInts(X2))
| ~ class_Int_Oring__char__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_853]),
[final] ).
cnf(i_0_1515,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_902]),
[final] ).
cnf(i_0_1516,plain,
( X1 = X3
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_903]),
[final] ).
cnf(i_0_1517,plain,
( X2 = X3
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_904]),
[final] ).
cnf(i_0_1518,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2) = 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_905]),
[final] ).
cnf(i_0_1519,plain,
~ c_member(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_906]),
[final] ).
cnf(i_0_1520,plain,
~ c_member(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_907]),
[final] ).
cnf(i_0_1521,plain,
( c_member(X3,X1,c_Set_Oinsert(X3,X2,X4))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_772]),
[final] ).
cnf(i_0_1522,plain,
( c_member(X3,X1,c_Set_Oinsert(X3,X2,X4))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_805]),
[final] ).
cnf(i_0_1523,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk26_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1524,plain,
( c_Finite__Set_Ocard(X1,esk44_3(X2,X3,X1)) = X2
| c_Finite__Set_Ocard(X1,X3) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_1525,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk41_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_699]),
[final] ).
cnf(i_0_1526,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,esk12_1(X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ c_member(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_909]),
[final] ).
cnf(i_0_1527,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,esk14_1(X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ c_member(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1528,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_844]),
[final] ).
cnf(i_0_1529,plain,
( X1 = hAPP(c_Nat_OSuc,esk23_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_850]),
[final] ).
cnf(i_0_1530,plain,
c_member(X1,X2,c_Set_Oinsert(X1,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_911]),
[final] ).
cnf(i_0_1531,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_896]),
[final] ).
cnf(i_0_1532,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_897]),
[final] ).
cnf(i_0_1533,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_912]),
[final] ).
cnf(i_0_1534,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1535,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1536,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_900]),
[final] ).
cnf(i_0_1537,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1538,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1539,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_863]),
[final] ).
cnf(i_0_1540,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_916]),
[final] ).
cnf(i_0_1541,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_917]),
[final] ).
cnf(i_0_1542,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_918]),
[final] ).
cnf(i_0_1543,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_919]),
[final] ).
cnf(i_0_1544,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| 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_768]),
[final] ).
cnf(i_0_1545,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),
inference(split_conjunct,[status(thm)],[i_0_920]),
[final] ).
cnf(i_0_1546,plain,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_921]),
[final] ).
cnf(i_0_1547,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_922]),
[final] ).
cnf(i_0_1548,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_923]),
[final] ).
cnf(i_0_1549,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_924]),
[final] ).
cnf(i_0_1550,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_925]),
[final] ).
cnf(i_0_1551,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_926]),
[final] ).
cnf(i_0_1552,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_865]),
[final] ).
cnf(i_0_1553,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_927]),
[final] ).
cnf(i_0_1554,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_928]),
[final] ).
cnf(i_0_1555,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_925]),
[final] ).
cnf(i_0_1556,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_926]),
[final] ).
cnf(i_0_1557,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_929]),
[final] ).
cnf(i_0_1558,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_849]),
[final] ).
cnf(i_0_1559,plain,
( c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,X3,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_845]),
[final] ).
cnf(i_0_1560,plain,
( c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,X3,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1561,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_931]),
[final] ).
cnf(i_0_1562,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_894]),
[final] ).
cnf(i_0_1563,plain,
( 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_834]),
[final] ).
cnf(i_0_1564,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_835]),
[final] ).
cnf(i_0_1565,plain,
( 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_836]),
[final] ).
cnf(i_0_1566,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| 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_837]),
[final] ).
cnf(i_0_1567,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_932]),
[final] ).
cnf(i_0_1568,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)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_933]),
[final] ).
cnf(i_0_1569,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))
| 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_934]),
[final] ).
cnf(i_0_1570,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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_935]),
[final] ).
cnf(i_0_1571,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_936]),
[final] ).
cnf(i_0_1572,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_937]),
[final] ).
cnf(i_0_1573,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_938]),
[final] ).
cnf(i_0_1574,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1575,plain,
( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_909]),
[final] ).
cnf(i_0_1576,plain,
( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk15_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1577,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_939]),
[final] ).
cnf(i_0_1578,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_940]),
[final] ).
cnf(i_0_1579,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_941]),
[final] ).
cnf(i_0_1580,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_937]),
[final] ).
cnf(i_0_1581,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_938]),
[final] ).
cnf(i_0_1582,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_942]),
[final] ).
cnf(i_0_1583,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_894]),
[final] ).
cnf(i_0_1584,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_888]),
[final] ).
cnf(i_0_1585,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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_943]),
[final] ).
cnf(i_0_1586,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_member(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_944]),
[final] ).
cnf(i_0_1587,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_member(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1588,plain,
( ~ c_member(X1,X2,X3)
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1589,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_846]),
[final] ).
cnf(i_0_1590,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_847]),
[final] ).
cnf(i_0_1591,plain,
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_947]),
[final] ).
cnf(i_0_1592,plain,
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_948]),
[final] ).
cnf(i_0_1593,plain,
( esk44_3(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Finite__Set_Ocard(X3,X2) != hAPP(c_Nat_OSuc,X1) ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_1594,plain,
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_949]),
[final] ).
cnf(i_0_1595,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)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_933]),
[final] ).
cnf(i_0_1596,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)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_933]),
[final] ).
cnf(i_0_1597,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| 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_934]),
[final] ).
cnf(i_0_1598,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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_934]),
[final] ).
cnf(i_0_1599,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_Set_Oinsert(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_950]),
[final] ).
cnf(i_0_1600,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_951]),
[final] ).
cnf(i_0_1601,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_952]),
[final] ).
cnf(i_0_1602,plain,
( hAPP(hAPP(X2,X4),X4) = X4
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_953]),
[final] ).
cnf(i_0_1603,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1604,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_927]),
[final] ).
cnf(i_0_1605,plain,
( c_member(X1,esk42_2(X2,X1),X2)
| c_Finite__Set_Ocard(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1606,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X1),
inference(split_conjunct,[status(thm)],[i_0_955]),
[final] ).
cnf(i_0_1607,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1608,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_1609,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_958]),
[final] ).
cnf(i_0_1610,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_959]),
[final] ).
cnf(i_0_1611,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_960]),
[final] ).
cnf(i_0_1612,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_961]),
[final] ).
cnf(i_0_1613,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_878]),
[final] ).
cnf(i_0_1614,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_962]),
[final] ).
cnf(i_0_1615,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1616,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_881]),
[final] ).
cnf(i_0_1617,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_964]),
[final] ).
cnf(i_0_1618,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_880]),
[final] ).
cnf(i_0_1619,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_965]),
[final] ).
cnf(i_0_1620,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_1621,plain,
( hBOOL(hAPP(X3,X2))
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_967]),
[final] ).
cnf(i_0_1622,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_968]),
[final] ).
cnf(i_0_1623,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_969]),
[final] ).
cnf(i_0_1624,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_970]),
[final] ).
cnf(i_0_1625,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)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_933]),
[final] ).
cnf(i_0_1626,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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_934]),
[final] ).
cnf(i_0_1627,plain,
c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1)) = 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_971]),
[final] ).
cnf(i_0_1628,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ 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_972]),
[final] ).
cnf(i_0_1629,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ 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_973]),
[final] ).
cnf(i_0_1630,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_974]),
[final] ).
cnf(i_0_1631,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_975]),
[final] ).
cnf(i_0_1632,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_member(X2,esk17_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1633,plain,
( c_member(X1,esk16_2(X2,X1),X2)
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1634,plain,
( X1 = hAPP(c_Nat_OSuc,esk22_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_976]),
[final] ).
cnf(i_0_1635,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_977]),
[final] ).
cnf(i_0_1636,plain,
c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_978]),
[final] ).
cnf(i_0_1637,plain,
c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_979]),
[final] ).
cnf(i_0_1638,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_980]),
[final] ).
cnf(i_0_1639,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| 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_981]),
[final] ).
cnf(i_0_1640,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1641,plain,
( c_member(X3,X2,X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_967]),
[final] ).
cnf(i_0_1642,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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_933]),
[final] ).
cnf(i_0_1643,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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_933]),
[final] ).
cnf(i_0_1644,plain,
( 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_934]),
[final] ).
cnf(i_0_1645,plain,
( 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_934]),
[final] ).
cnf(i_0_1646,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[i_0_983]),
[final] ).
cnf(i_0_1647,plain,
( X2 = X3
| ~ c_member(X1,X2,c_fequal(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_984]),
[final] ).
cnf(i_0_1648,plain,
( 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_863]),
[final] ).
cnf(i_0_1649,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_926]),
[final] ).
cnf(i_0_1650,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_878]),
[final] ).
cnf(i_0_1651,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_985]),
[final] ).
cnf(i_0_1652,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_986]),
[final] ).
cnf(i_0_1653,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_987]),
[final] ).
cnf(i_0_1654,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1655,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1656,plain,
( ~ 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_988]),
[final] ).
cnf(i_0_1657,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1658,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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_990]),
[final] ).
cnf(i_0_1659,plain,
~ 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_991]),
[final] ).
cnf(i_0_1660,plain,
( c_member(tc_Nat_Onat,esk15_2(X1,X2),X1)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1661,plain,
( c_member(tc_Nat_Onat,esk13_2(X1,X2),X1)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_909]),
[final] ).
cnf(i_0_1662,plain,
( X1 = c_Groups_Ozero__class_Ozero(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_992]),
[final] ).
cnf(i_0_1663,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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_992]),
[final] ).
cnf(i_0_1664,plain,
( ~ 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_993]),
[final] ).
cnf(i_0_1665,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_994]),
[final] ).
cnf(i_0_1666,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_995]),
[final] ).
cnf(i_0_1667,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_996]),
[final] ).
cnf(i_0_1668,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_997]),
[final] ).
cnf(i_0_1669,plain,
( 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_943]),
[final] ).
cnf(i_0_1670,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_938]),
[final] ).
cnf(i_0_1671,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1672,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_999]),
[final] ).
cnf(i_0_1673,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_975]),
[final] ).
cnf(i_0_1674,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_975]),
[final] ).
cnf(i_0_1675,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_1000]),
[final] ).
cnf(i_0_1676,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1001]),
[final] ).
cnf(i_0_1677,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1002]),
[final] ).
cnf(i_0_1678,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_1003]),
[final] ).
cnf(i_0_1679,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_1004]),
[final] ).
cnf(i_0_1680,plain,
( 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_850]),
[final] ).
cnf(i_0_1681,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1005]),
[final] ).
cnf(i_0_1682,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1005]),
[final] ).
cnf(i_0_1683,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1684,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1685,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1006]),
[final] ).
cnf(i_0_1686,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_851]),
[final] ).
cnf(i_0_1687,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1007]),
[final] ).
cnf(i_0_1688,plain,
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_1008]),
[final] ).
cnf(i_0_1689,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1690,plain,
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_1009]),
[final] ).
cnf(i_0_1691,plain,
( 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_976]),
[final] ).
cnf(i_0_1692,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(split_conjunct,[status(thm)],[i_0_1010]),
[final] ).
cnf(i_0_1693,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Finite__Set_Ocard(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1011]),
[final] ).
cnf(i_0_1694,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[i_0_1012]),
[final] ).
cnf(i_0_1695,plain,
( 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_981]),
[final] ).
cnf(i_0_1696,plain,
( c_Groups_Ozero__class_Ozero(X2) = 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_982]),
[final] ).
cnf(i_0_1697,plain,
( 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_1013]),
[final] ).
cnf(i_0_1698,plain,
( 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_1014]),
[final] ).
cnf(i_0_1699,plain,
( 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_1015]),
[final] ).
cnf(i_0_1700,plain,
( 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_1016]),
[final] ).
cnf(i_0_1701,plain,
( 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_1017]),
[final] ).
cnf(i_0_1702,plain,
( X3 = 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_983]),
[final] ).
cnf(i_0_1703,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_fequal(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1704,plain,
( 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_1019]),
[final] ).
cnf(i_0_1705,plain,
( 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_1020]),
[final] ).
cnf(i_0_1706,plain,
( 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_1021]),
[final] ).
cnf(i_0_1707,plain,
( 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_1022]),
[final] ).
cnf(i_0_1708,plain,
( 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_1023]),
[final] ).
cnf(i_0_1709,plain,
( 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_1024]),
[final] ).
cnf(i_0_1710,plain,
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_1025]),
[final] ).
cnf(i_0_1711,plain,
hAPP(c_Nat_OSuc,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_1026]),
[final] ).
cnf(i_0_1712,plain,
hAPP(c_Nat_OSuc,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_1027]),
[final] ).
cnf(i_0_1713,plain,
( 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_1028]),
[final] ).
cnf(i_0_1714,plain,
( 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_1029]),
[final] ).
cnf(i_0_1715,plain,
( 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_992]),
[final] ).
cnf(i_0_1716,plain,
c_Finite__Set_Ofinite(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1717,plain,
c_Finite__Set_Ofinite(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_1031]),
[final] ).
cnf(i_0_1718,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_870]),
[final] ).
cnf(i_0_1719,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_870]),
[final] ).
cnf(i_0_1720,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1032]),
[final] ).
cnf(i_0_1721,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_925]),
[final] ).
cnf(i_0_1722,plain,
( c_member(X3,X1,c_fequal(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_984]),
[final] ).
cnf(i_0_1723,plain,
( 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_990]),
[final] ).
cnf(i_0_1724,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1033]),
[final] ).
cnf(i_0_1725,plain,
( 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_1011]),
[final] ).
cnf(i_0_1726,plain,
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_1727,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1728,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1034]),
[final] ).
cnf(i_0_1729,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_finite__indi]),
[final] ).
cnf(i_0_1730,plain,
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_1035]),
[final] ).
cnf(i_0_1731,plain,
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_1036]),
[final] ).
cnf(i_0_1732,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_940]),
[final] ).
cnf(i_0_1733,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_937]),
[final] ).
cnf(i_0_1734,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1735,plain,
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_1038]),
[final] ).
cnf(i_0_1736,plain,
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_1039]),
[final] ).
cnf(i_0_1737,plain,
( X2 = X3
| c_SetInterval_Oord__class_OgreaterThan(X1,X2) != c_SetInterval_Oord__class_OgreaterThan(X1,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1738,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1739,plain,
( 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)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1740,plain,
( hBOOL(hAPP(c_fequal(X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1741,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_1043]),
[final] ).
cnf(i_0_1742,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_1044]),
[final] ).
cnf(i_0_1743,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_1045]),
[final] ).
cnf(i_0_1744,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1046]),
[final] ).
cnf(i_0_1745,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1047]),
[final] ).
cnf(i_0_1746,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1747,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1748,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1749,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1051]),
[final] ).
cnf(i_0_1750,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1052]),
[final] ).
cnf(i_0_1751,plain,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1011]),
[final] ).
cnf(i_0_1752,plain,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1053]),
[final] ).
cnf(i_0_1753,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1054]),
[final] ).
cnf(i_0_1754,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1055]),
[final] ).
cnf(i_0_1755,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1056]),
[final] ).
cnf(i_0_1756,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1057]),
[final] ).
cnf(i_0_1757,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1058]),
[final] ).
cnf(i_0_1758,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1059]),
[final] ).
cnf(i_0_1759,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1060]),
[final] ).
cnf(i_0_1760,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1061]),
[final] ).
cnf(i_0_1761,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1062]),
[final] ).
cnf(i_0_1762,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1063]),
[final] ).
cnf(i_0_1763,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_1064]),
[final] ).
cnf(i_0_1764,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_1065]),
[final] ).
cnf(i_0_1765,plain,
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_1766,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_1767,plain,
( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1066]),
[final] ).
cnf(i_0_1768,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_1067]),
[final] ).
cnf(i_0_1769,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_1770,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_1771,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_1772,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_1773,plain,
~ hBOOL(c_fFalse),
inference(split_conjunct,[status(thm)],[i_0_1068]),
[final] ).
cnf(i_0_1774,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_1775,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_1776,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_1777,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_1778,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_1779,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_1780,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_1781,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_1782,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_1783,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_1784,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_1785,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_1786,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_1787,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_1788,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1789,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1790,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1791,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1792,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1793,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]),
[final] ).
cnf(i_0_1794,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]),
[final] ).
cnf(i_0_1795,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1796,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1797,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_1798,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_1799,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1800,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1801,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_1802,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
[final] ).
cnf(i_0_1803,plain,
hBOOL(c_fTrue),
inference(split_conjunct,[status(thm)],[help_c__fTrue__1]),
[final] ).
cnf(i_0_1804,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[i_0_1069]),
[final] ).
cnf(i_0_1805,axiom,
X1 = X1 ).
cnf(i_0_1806,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1807,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1808,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3,X4,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3,X4,X5) ) ).
cnf(i_0_1809,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1,X4,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2,X4,X5) ) ).
cnf(i_0_1810,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X1,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X2,X5) ) ).
cnf(i_0_1811,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X5,X1) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X5,X2) ) ).
cnf(i_0_1812,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1813,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1814,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1815,axiom,
( X1 != X2
| esk5_5(X1,X3,X4,X5,X6) = esk5_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1816,axiom,
( X1 != X2
| esk5_5(X3,X1,X4,X5,X6) = esk5_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1817,axiom,
( X1 != X2
| esk5_5(X3,X4,X1,X5,X6) = esk5_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1818,axiom,
( X1 != X2
| esk5_5(X3,X4,X5,X1,X6) = esk5_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1819,axiom,
( X1 != X2
| esk5_5(X3,X4,X5,X6,X1) = esk5_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1820,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1821,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).
cnf(i_0_1822,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).
cnf(i_0_1823,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).
cnf(i_0_1824,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1825,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1826,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_1827,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_1828,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_1829,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_1830,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1831,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1832,axiom,
( X1 != X2
| esk4_4(X1,X3,X4,X5) = esk4_4(X2,X3,X4,X5) ) ).
cnf(i_0_1833,axiom,
( X1 != X2
| esk4_4(X3,X1,X4,X5) = esk4_4(X3,X2,X4,X5) ) ).
cnf(i_0_1834,axiom,
( X1 != X2
| esk4_4(X3,X4,X1,X5) = esk4_4(X3,X4,X2,X5) ) ).
cnf(i_0_1835,axiom,
( X1 != X2
| esk4_4(X3,X4,X5,X1) = esk4_4(X3,X4,X5,X2) ) ).
cnf(i_0_1836,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1837,axiom,
( X1 != X2
| esk2_4(X1,X3,X4,X5) = esk2_4(X2,X3,X4,X5) ) ).
cnf(i_0_1838,axiom,
( X1 != X2
| esk2_4(X3,X1,X4,X5) = esk2_4(X3,X2,X4,X5) ) ).
cnf(i_0_1839,axiom,
( X1 != X2
| esk2_4(X3,X4,X1,X5) = esk2_4(X3,X4,X2,X5) ) ).
cnf(i_0_1840,axiom,
( X1 != X2
| esk2_4(X3,X4,X5,X1) = esk2_4(X3,X4,X5,X2) ) ).
cnf(i_0_1841,axiom,
( X1 != X2
| esk3_4(X1,X3,X4,X5) = esk3_4(X2,X3,X4,X5) ) ).
cnf(i_0_1842,axiom,
( X1 != X2
| esk3_4(X3,X1,X4,X5) = esk3_4(X3,X2,X4,X5) ) ).
cnf(i_0_1843,axiom,
( X1 != X2
| esk3_4(X3,X4,X1,X5) = esk3_4(X3,X4,X2,X5) ) ).
cnf(i_0_1844,axiom,
( X1 != X2
| esk3_4(X3,X4,X5,X1) = esk3_4(X3,X4,X5,X2) ) ).
cnf(i_0_1845,axiom,
( X1 != X2
| esk30_4(X1,X3,X4,X5) = esk30_4(X2,X3,X4,X5) ) ).
cnf(i_0_1846,axiom,
( X1 != X2
| esk30_4(X3,X1,X4,X5) = esk30_4(X3,X2,X4,X5) ) ).
cnf(i_0_1847,axiom,
( X1 != X2
| esk30_4(X3,X4,X1,X5) = esk30_4(X3,X4,X2,X5) ) ).
cnf(i_0_1848,axiom,
( X1 != X2
| esk30_4(X3,X4,X5,X1) = esk30_4(X3,X4,X5,X2) ) ).
cnf(i_0_1849,axiom,
( X1 != X2
| esk40_4(X1,X3,X4,X5) = esk40_4(X2,X3,X4,X5) ) ).
cnf(i_0_1850,axiom,
( X1 != X2
| esk40_4(X3,X1,X4,X5) = esk40_4(X3,X2,X4,X5) ) ).
cnf(i_0_1851,axiom,
( X1 != X2
| esk40_4(X3,X4,X1,X5) = esk40_4(X3,X4,X2,X5) ) ).
cnf(i_0_1852,axiom,
( X1 != X2
| esk40_4(X3,X4,X5,X1) = esk40_4(X3,X4,X5,X2) ) ).
cnf(i_0_1853,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1854,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1855,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1856,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1857,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1858,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1859,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1860,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1861,axiom,
( X1 != X2
| esk29_3(X1,X3,X4) = esk29_3(X2,X3,X4) ) ).
cnf(i_0_1862,axiom,
( X1 != X2
| esk29_3(X3,X1,X4) = esk29_3(X3,X2,X4) ) ).
cnf(i_0_1863,axiom,
( X1 != X2
| esk29_3(X3,X4,X1) = esk29_3(X3,X4,X2) ) ).
cnf(i_0_1864,axiom,
( X1 != X2
| esk39_3(X1,X3,X4) = esk39_3(X2,X3,X4) ) ).
cnf(i_0_1865,axiom,
( X1 != X2
| esk39_3(X3,X1,X4) = esk39_3(X3,X2,X4) ) ).
cnf(i_0_1866,axiom,
( X1 != X2
| esk39_3(X3,X4,X1) = esk39_3(X3,X4,X2) ) ).
cnf(i_0_1867,axiom,
( X1 != X2
| esk44_3(X1,X3,X4) = esk44_3(X2,X3,X4) ) ).
cnf(i_0_1868,axiom,
( X1 != X2
| esk44_3(X3,X1,X4) = esk44_3(X3,X2,X4) ) ).
cnf(i_0_1869,axiom,
( X1 != X2
| esk44_3(X3,X4,X1) = esk44_3(X3,X4,X2) ) ).
cnf(i_0_1870,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1871,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1872,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1873,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThan(X1,X3) = c_SetInterval_Oord__class_OgreaterThan(X2,X3) ) ).
cnf(i_0_1874,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThan(X3,X1) = c_SetInterval_Oord__class_OgreaterThan(X3,X2) ) ).
cnf(i_0_1875,axiom,
( X1 != X2
| c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).
cnf(i_0_1876,axiom,
( X1 != X2
| c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1886,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_1887,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_1888,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_1889,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_1890,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_1891,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_1892,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
| c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
| c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
| c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).
cnf(i_0_1904,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1905,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_1906,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1907,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1908,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1909,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1913,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1914,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_1915,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1916,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1917,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1918,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_1919,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_1920,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1921,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1922,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1923,axiom,
( X1 != X2
| ~ c_member(X1,X3,X4)
| c_member(X2,X3,X4) ) ).
cnf(i_0_1924,axiom,
( X1 != X2
| ~ c_member(X3,X1,X4)
| c_member(X3,X2,X4) ) ).
cnf(i_0_1925,axiom,
( X1 != X2
| ~ c_member(X3,X4,X1)
| c_member(X3,X4,X2) ) ).
cnf(i_0_1926,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1927,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1928,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_1932,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
| c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).
cnf(i_0_1933,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
| c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).
cnf(i_0_1934,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
| c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).
cnf(i_0_1935,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1936,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1937,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1805_001,axiom,
X1 = X1 ).
cnf(i_0_1806_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1807_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1808_004,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3,X4,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3,X4,X5) ) ).
cnf(i_0_1809_005,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1,X4,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2,X4,X5) ) ).
cnf(i_0_1810_006,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X1,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X2,X5) ) ).
cnf(i_0_1811_007,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X5,X1) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X5,X2) ) ).
cnf(i_0_1812_008,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1813_009,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1814_010,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1815_011,axiom,
( X1 != X2
| esk5_5(X1,X3,X4,X5,X6) = esk5_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1816_012,axiom,
( X1 != X2
| esk5_5(X3,X1,X4,X5,X6) = esk5_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1817_013,axiom,
( X1 != X2
| esk5_5(X3,X4,X1,X5,X6) = esk5_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1818_014,axiom,
( X1 != X2
| esk5_5(X3,X4,X5,X1,X6) = esk5_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1819_015,axiom,
( X1 != X2
| esk5_5(X3,X4,X5,X6,X1) = esk5_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1820_016,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1821_017,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).
cnf(i_0_1822_018,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).
cnf(i_0_1823_019,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).
cnf(i_0_1824_020,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1825_021,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1826_022,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_1827_023,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_1828_024,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_1829_025,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_1830_026,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1831_027,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1832_028,axiom,
( X1 != X2
| esk4_4(X1,X3,X4,X5) = esk4_4(X2,X3,X4,X5) ) ).
cnf(i_0_1833_029,axiom,
( X1 != X2
| esk4_4(X3,X1,X4,X5) = esk4_4(X3,X2,X4,X5) ) ).
cnf(i_0_1834_030,axiom,
( X1 != X2
| esk4_4(X3,X4,X1,X5) = esk4_4(X3,X4,X2,X5) ) ).
cnf(i_0_1835_031,axiom,
( X1 != X2
| esk4_4(X3,X4,X5,X1) = esk4_4(X3,X4,X5,X2) ) ).
cnf(i_0_1836_032,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1837_033,axiom,
( X1 != X2
| esk2_4(X1,X3,X4,X5) = esk2_4(X2,X3,X4,X5) ) ).
cnf(i_0_1838_034,axiom,
( X1 != X2
| esk2_4(X3,X1,X4,X5) = esk2_4(X3,X2,X4,X5) ) ).
cnf(i_0_1839_035,axiom,
( X1 != X2
| esk2_4(X3,X4,X1,X5) = esk2_4(X3,X4,X2,X5) ) ).
cnf(i_0_1840_036,axiom,
( X1 != X2
| esk2_4(X3,X4,X5,X1) = esk2_4(X3,X4,X5,X2) ) ).
cnf(i_0_1841_037,axiom,
( X1 != X2
| esk3_4(X1,X3,X4,X5) = esk3_4(X2,X3,X4,X5) ) ).
cnf(i_0_1842_038,axiom,
( X1 != X2
| esk3_4(X3,X1,X4,X5) = esk3_4(X3,X2,X4,X5) ) ).
cnf(i_0_1843_039,axiom,
( X1 != X2
| esk3_4(X3,X4,X1,X5) = esk3_4(X3,X4,X2,X5) ) ).
cnf(i_0_1844_040,axiom,
( X1 != X2
| esk3_4(X3,X4,X5,X1) = esk3_4(X3,X4,X5,X2) ) ).
cnf(i_0_1845_041,axiom,
( X1 != X2
| esk30_4(X1,X3,X4,X5) = esk30_4(X2,X3,X4,X5) ) ).
cnf(i_0_1846_042,axiom,
( X1 != X2
| esk30_4(X3,X1,X4,X5) = esk30_4(X3,X2,X4,X5) ) ).
cnf(i_0_1847_043,axiom,
( X1 != X2
| esk30_4(X3,X4,X1,X5) = esk30_4(X3,X4,X2,X5) ) ).
cnf(i_0_1848_044,axiom,
( X1 != X2
| esk30_4(X3,X4,X5,X1) = esk30_4(X3,X4,X5,X2) ) ).
cnf(i_0_1849_045,axiom,
( X1 != X2
| esk40_4(X1,X3,X4,X5) = esk40_4(X2,X3,X4,X5) ) ).
cnf(i_0_1850_046,axiom,
( X1 != X2
| esk40_4(X3,X1,X4,X5) = esk40_4(X3,X2,X4,X5) ) ).
cnf(i_0_1851_047,axiom,
( X1 != X2
| esk40_4(X3,X4,X1,X5) = esk40_4(X3,X4,X2,X5) ) ).
cnf(i_0_1852_048,axiom,
( X1 != X2
| esk40_4(X3,X4,X5,X1) = esk40_4(X3,X4,X5,X2) ) ).
cnf(i_0_1853_049,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1854_050,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1855_051,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1856_052,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1857_053,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1858_054,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1859_055,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1860_056,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1861_057,axiom,
( X1 != X2
| esk29_3(X1,X3,X4) = esk29_3(X2,X3,X4) ) ).
cnf(i_0_1862_058,axiom,
( X1 != X2
| esk29_3(X3,X1,X4) = esk29_3(X3,X2,X4) ) ).
cnf(i_0_1863_059,axiom,
( X1 != X2
| esk29_3(X3,X4,X1) = esk29_3(X3,X4,X2) ) ).
cnf(i_0_1864_060,axiom,
( X1 != X2
| esk39_3(X1,X3,X4) = esk39_3(X2,X3,X4) ) ).
cnf(i_0_1865_061,axiom,
( X1 != X2
| esk39_3(X3,X1,X4) = esk39_3(X3,X2,X4) ) ).
cnf(i_0_1866_062,axiom,
( X1 != X2
| esk39_3(X3,X4,X1) = esk39_3(X3,X4,X2) ) ).
cnf(i_0_1867_063,axiom,
( X1 != X2
| esk44_3(X1,X3,X4) = esk44_3(X2,X3,X4) ) ).
cnf(i_0_1868_064,axiom,
( X1 != X2
| esk44_3(X3,X1,X4) = esk44_3(X3,X2,X4) ) ).
cnf(i_0_1869_065,axiom,
( X1 != X2
| esk44_3(X3,X4,X1) = esk44_3(X3,X4,X2) ) ).
cnf(i_0_1870_066,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1871_067,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1872_068,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1873_069,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThan(X1,X3) = c_SetInterval_Oord__class_OgreaterThan(X2,X3) ) ).
cnf(i_0_1874_070,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThan(X3,X1) = c_SetInterval_Oord__class_OgreaterThan(X3,X2) ) ).
cnf(i_0_1875_071,axiom,
( X1 != X2
| c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).
cnf(i_0_1876_072,axiom,
( X1 != X2
| c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).
cnf(i_0_1877_073,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1878_074,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1879_075,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1880_076,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1881_077,axiom,
( X1 != X2
| c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).
cnf(i_0_1882_078,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1883_079,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1884_080,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1885_081,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1886_082,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_1887_083,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_1888_084,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_1889_085,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_1890_086,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_1891_087,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_1892_088,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1893_089,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1894_090,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1895_091,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1896_092,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1897_093,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1898_094,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1899_095,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1900_096,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1901_097,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
| c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).
cnf(i_0_1902_098,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
| c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).
cnf(i_0_1903_099,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
| c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).
cnf(i_0_1904_100,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1905_101,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_1906_102,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1907_103,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1908_104,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1909_105,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1910_106,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1911_107,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1912_108,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1913_109,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1914_110,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_1915_111,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1916_112,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1917_113,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1918_114,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_1919_115,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_1920_116,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1921_117,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1922_118,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1923_119,axiom,
( X1 != X2
| ~ c_member(X1,X3,X4)
| c_member(X2,X3,X4) ) ).
cnf(i_0_1924_120,axiom,
( X1 != X2
| ~ c_member(X3,X1,X4)
| c_member(X3,X2,X4) ) ).
cnf(i_0_1925_121,axiom,
( X1 != X2
| ~ c_member(X3,X4,X1)
| c_member(X3,X4,X2) ) ).
cnf(i_0_1926_122,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1927_123,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1928_124,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1929_125,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_1930_126,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_1931_127,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_1932_128,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
| c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).
cnf(i_0_1933_129,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
| c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).
cnf(i_0_1934_130,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
| c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).
cnf(i_0_1935_131,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1936_132,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1937_133,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1938,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ class_Groups_Ocomm__monoid__add(X5)
| c_member(X1,esk33_8(X6,X7,c_Set_Oimage(X1,X2,X3,X4),X4,X3,X2,X1,X5),X4)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X5,X6,c_Set_Oimage(X1,X2,X3,X4)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5,X7,X4) ),
inference(equality_inference,[],[1072]) ).
cnf(i_0_1939,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk9_4(X3,X1,X2,c_Set_Oimage(X1,X2,X4,X3)),c_Set_Oimage(X1,X2,X4,X3)),X3)
| c_Set_Oimage(X1,X2,X4,X3) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(equality_inference,[],[1101]) ).
cnf(i_0_1940,plain,
( X1 = esk4_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)))
| ~ c_member(X3,hAPP(X2,X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))) ),
inference(equality_inference,[],[1103]) ).
cnf(i_0_1941,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[1121]) ).
cnf(i_0_1942,plain,
( c_Fun_Oinj__on(X1,X2,esk9_4(X3,X2,X1,c_Set_Oimage(X2,X1,X4,X3)),c_Set_Oimage(X2,X1,X4,X3))
| c_Set_Oimage(X2,X1,X4,X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(equality_inference,[],[1129]) ).
cnf(i_0_1943,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X3,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X4,X5) ),
inference(equality_inference,[],[1135]) ).
cnf(i_0_1944,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_member(X1,X5,X4)
| hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5 ),
inference(equality_inference,[],[1140]) ).
cnf(i_0_1945,plain,
( ~ c_member(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_member(X1,esk30_4(c_Nat_OSuc,X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
| 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)) ),
inference(equality_inference,[],[1141]) ).
cnf(i_0_1946,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1161]) ).
cnf(i_0_1947,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1162]) ).
cnf(i_0_1948,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1163]) ).
cnf(i_0_1949,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1164]) ).
cnf(i_0_1950,plain,
c_member(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),
inference(equality_inference,[],[1178]) ).
cnf(i_0_1951,plain,
( ~ c_member(X1,X2,X3)
| c_member(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3)) ),
inference(equality_inference,[],[1183]) ).
cnf(i_0_1952,plain,
( ~ c_member(X1,X2,X3)
| ~ c_member(X1,X2,X3)
| X2 = X2
| ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
inference(equality_inference,[],[1189]) ).
cnf(i_0_1953,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[1216]) ).
cnf(i_0_1954,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(equality_inference,[],[1294]) ).
cnf(i_0_1955,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(equality_inference,[],[1295]) ).
cnf(i_0_1956,plain,
X1 = X1,
inference(equality_inference,[],[1308]) ).
cnf(i_0_1957,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(equality_inference,[],[1332]) ).
cnf(i_0_1958,plain,
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,[],[1333]) ).
cnf(i_0_1959,plain,
( c_member(X1,X2,X3)
| X3 = X3
| c_member(X1,X2,X3) ),
inference(equality_inference,[],[1365]) ).
cnf(i_0_1960,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(equality_inference,[],[1386]) ).
cnf(i_0_1961,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(equality_inference,[],[1396]) ).
cnf(i_0_1962,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(equality_inference,[],[1417]) ).
cnf(i_0_1963,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)) ),
inference(equality_inference,[],[1478]) ).
cnf(i_0_1964,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[1481]) ).
cnf(i_0_1965,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[1482]) ).
cnf(i_0_1966,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[1484]) ).
cnf(i_0_1967,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(equality_inference,[],[1506]) ).
cnf(i_0_1968,plain,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2) = c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(equality_inference,[],[1513]) ).
cnf(i_0_1969,plain,
( ~ class_Int_Oring__char__0(X1)
| ~ c_member(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Oring__1__class_OInts(X1))
| 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,[],[1514]) ).
cnf(i_0_1970,plain,
X1 = X1,
inference(equality_inference,[],[1516]) ).
cnf(i_0_1971,plain,
X1 = X1,
inference(equality_inference,[],[1517]) ).
cnf(i_0_1972,plain,
c_member(X1,X2,c_Set_Oinsert(X1,X2,X3)),
inference(equality_inference,[],[1522]) ).
cnf(i_0_1973,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(equality_inference,[],[1574]) ).
cnf(i_0_1974,plain,
~ c_member(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(equality_inference,[],[1588]) ).
cnf(i_0_1975,plain,
X1 = X1,
inference(equality_inference,[],[1601]) ).
cnf(i_0_1976,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1603]) ).
cnf(i_0_1977,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X2)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[1604]) ).
cnf(i_0_1978,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[1651]) ).
cnf(i_0_1979,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[1653]) ).
cnf(i_0_1980,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[1654]) ).
cnf(i_0_1981,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[1655]) ).
cnf(i_0_1982,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[1664]) ).
cnf(i_0_1983,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1673]) ).
cnf(i_0_1984,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1674]) ).
cnf(i_0_1985,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(equality_inference,[],[1680]) ).
cnf(i_0_1986,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1686]) ).
cnf(i_0_1987,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1687]) ).
cnf(i_0_1988,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(equality_inference,[],[1689]) ).
cnf(i_0_1989,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(equality_inference,[],[1691]) ).
cnf(i_0_1990,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| 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,[],[1695]) ).
cnf(i_0_1991,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[1696]) ).
cnf(i_0_1992,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[1702]) ).
cnf(i_0_1993,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[1719]) ).
cnf(i_0_1994,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[1720]) ).
cnf(i_0_1995,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[1721]) ).
cnf(i_0_1996,plain,
c_member(X1,X2,c_fequal(X2)),
inference(equality_inference,[],[1722]) ).
cnf(i_0_1997,plain,
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,[],[1725]) ).
cnf(i_0_1998,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1734]) ).
cnf(i_0_1999,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X2 ),
inference(equality_inference,[],[1737]) ).
cnf(i_0_2000,plain,
hBOOL(hAPP(c_fequal(X1),X1)),
inference(equality_inference,[],[1740]) ).
cnf(i_0_2001,plain,
X1 = X1,
inference(equality_inference,[],[1745]) ).
cnf(i_0_2002,plain,
( ~ c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
| c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
inference(scs_inference,[],[i_0_1804,i_0_1127]) ).
cnf(i_0_2003,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(scs_inference,[],[i_0_1768,i_0_1806]) ).
cnf(i_0_2004,plain,
X1 != hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(scs_inference,[],[i_0_1768,i_0_1363,i_0_1806,i_0_1673]) ).
cnf(i_0_2005,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_1673]) ).
cnf(i_0_2006,plain,
hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X1,
inference(scs_inference,[],[i_0_1768,i_0_1363,i_0_1806,i_0_1673,i_0_1674]) ).
cnf(i_0_2007,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(rename_variables,[],[i_0_1674]) ).
cnf(i_0_2008,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) != X1,
inference(scs_inference,[],[i_0_1768,i_0_1397,i_0_1363,i_0_1806,i_0_1673,i_0_1674,i_0_1689]) ).
cnf(i_0_2009,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(rename_variables,[],[i_0_1397]) ).
cnf(i_0_2010,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1689]) ).
cnf(i_0_2011,plain,
c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,X2),
inference(scs_inference,[],[i_0_1967,i_0_1768,i_0_1397,i_0_1363,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691]) ).
cnf(i_0_2012,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(rename_variables,[],[i_0_1691]) ).
cnf(i_0_2013,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),
inference(scs_inference,[],[i_0_1967,i_0_1768,i_0_1397,i_0_1363,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825]) ).
cnf(i_0_2014,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,c_Set_Oimage(X1,X4,X3,X2),X4),X2),
inference(scs_inference,[],[i_0_1692,i_0_1967,i_0_1768,i_0_1397,i_0_1363,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088]) ).
cnf(i_0_2015,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1692]) ).
cnf(i_0_2016,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X3,X1,X4,X5))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),esk19_5(X5,X4,X3,X2,X1),X5) ),
inference(rename_variables,[],[i_0_1088]) ).
cnf(i_0_2017,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1692,i_0_1967,i_0_1768,i_0_1520,i_0_1397,i_0_1363,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114]) ).
cnf(i_0_2018,plain,
~ c_member(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rename_variables,[],[i_0_1520]) ).
cnf(i_0_2019,plain,
( c_member(X1,esk18_4(X2,X3,X1,X4),X2)
| ~ c_member(X5,X4,c_Set_Oimage(X1,X5,X3,X2)) ),
inference(rename_variables,[],[i_0_1114]) ).
cnf(i_0_2020,plain,
~ c_member(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Set_Oimage(X2,X1,c_Nat_OSuc,X3)),
inference(scs_inference,[],[i_0_1692,i_0_1967,i_0_1768,i_0_1520,i_0_1397,i_0_1758,i_0_1363,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115]) ).
cnf(i_0_2021,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1758]) ).
cnf(i_0_2022,plain,
( X1 = hAPP(X2,esk18_4(X3,X2,X4,X1))
| ~ c_member(X5,X1,c_Set_Oimage(X4,X5,X2,X3)) ),
inference(rename_variables,[],[i_0_1115]) ).
cnf(i_0_2023,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X3,c_Set_Oinsert(X2,X5,X4))),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_1520,i_0_1397,i_0_1758,i_0_1363,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125]) ).
cnf(i_0_2024,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2),c_Set_Oimage(X1,X4,X5,X3)) ),
inference(rename_variables,[],[i_0_1125]) ).
cnf(i_0_2025,plain,
c_member(X1,X2,c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4))),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_1520,i_0_1397,i_0_1758,i_0_1363,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302]) ).
cnf(i_0_2026,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_2027,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X3),X4)
| c_member(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1302]) ).
cnf(i_0_2028,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X3,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_1520,i_0_1397,i_0_1758,i_0_1363,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332]) ).
cnf(i_0_2029,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2030,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = c_Set_Oimage(X2,X3,X4,X1) ),
inference(rename_variables,[],[i_0_1332]) ).
cnf(i_0_2031,plain,
c_Set_Oimage(X1,X2,X3,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_2029,i_0_1520,i_0_1397,i_0_1758,i_0_1363,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333]) ).
cnf(i_0_2032,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2033,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X2,X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_1333]) ).
cnf(i_0_2034,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_2029,i_0_1520,i_0_1397,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348]) ).
cnf(i_0_2035,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(rename_variables,[],[i_0_1364]) ).
cnf(i_0_2036,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1348]) ).
cnf(i_0_2037,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_2029,i_0_1520,i_0_1397,i_0_1542,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351]) ).
cnf(i_0_2038,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_1542]) ).
cnf(i_0_2039,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1351]) ).
cnf(i_0_2040,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3)),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_2029,i_0_1520,i_0_1397,i_0_1542,i_0_2038,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352]) ).
cnf(i_0_2041,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_1542]) ).
cnf(i_0_2042,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1352]) ).
cnf(i_0_2043,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Finite__Set_Ocard(X2,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_2029,i_0_1520,i_0_1397,i_0_1542,i_0_2038,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388]) ).
cnf(i_0_2044,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk27_2(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1388]) ).
cnf(i_0_2045,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X1),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_2029,i_0_1520,i_0_1397,i_0_2009,i_0_1542,i_0_2038,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410]) ).
cnf(i_0_2046,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(rename_variables,[],[i_0_1397]) ).
cnf(i_0_2047,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1410]) ).
cnf(i_0_2048,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X2),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_2029,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412]) ).
cnf(i_0_2049,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(rename_variables,[],[i_0_1397]) ).
cnf(i_0_2050,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1412]) ).
cnf(i_0_2051,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_2029,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_1606,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414]) ).
cnf(i_0_2052,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X1),
inference(rename_variables,[],[i_0_1606]) ).
cnf(i_0_2053,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1414]) ).
cnf(i_0_2054,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X2),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_2029,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_1606,i_0_2052,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416]) ).
cnf(i_0_2055,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X1),
inference(rename_variables,[],[i_0_1606]) ).
cnf(i_0_2056,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1416]) ).
cnf(i_0_2057,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1768,i_0_2029,i_0_2032,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_1606,i_0_2052,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417]) ).
cnf(i_0_2058,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2059,plain,
( X1 != hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1417]) ).
cnf(i_0_2060,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_1606,i_0_2052,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429]) ).
cnf(i_0_2061,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1761]) ).
cnf(i_0_2062,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
inference(rename_variables,[],[i_0_1429]) ).
cnf(i_0_2063,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_1606,i_0_2052,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443]) ).
cnf(i_0_2064,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(rename_variables,[],[i_0_1363]) ).
cnf(i_0_2065,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1443]) ).
cnf(i_0_2066,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X1),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1606,i_0_2052,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447]) ).
cnf(i_0_2067,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_1542]) ).
cnf(i_0_2068,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1447]) ).
cnf(i_0_2069,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),X2),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1606,i_0_2052,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448]) ).
cnf(i_0_2070,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1448]) ).
cnf(i_0_2071,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X2),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1606,i_0_2052,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473]) ).
cnf(i_0_2072,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1473]) ).
cnf(i_0_2073,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1606,i_0_2052,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506]) ).
cnf(i_0_2074,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2075,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1)) ),
inference(rename_variables,[],[i_0_1506]) ).
cnf(i_0_2076,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1606,i_0_2052,i_0_1694,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507]) ).
cnf(i_0_2077,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(rename_variables,[],[i_0_1694]) ).
cnf(i_0_2078,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1507]) ).
cnf(i_0_2079,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_1694,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510]) ).
cnf(i_0_2080,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_2081,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1510]) ).
cnf(i_0_2082,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_1694,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511]) ).
cnf(i_0_2083,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1738]) ).
cnf(i_0_2084,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1511]) ).
cnf(i_0_2085,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))),
inference(scs_inference,[],[i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_1694,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512]) ).
cnf(i_0_2086,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1512]) ).
cnf(i_0_2087,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X1),
inference(scs_inference,[],[i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_1694,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535]) ).
cnf(i_0_2088,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1677]) ).
cnf(i_0_2089,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1535]) ).
cnf(i_0_2090,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(scs_inference,[],[i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_1694,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537]) ).
cnf(i_0_2091,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1537]) ).
cnf(i_0_2092,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X1),
inference(scs_inference,[],[i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539]) ).
cnf(i_0_2093,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X1),
inference(rename_variables,[],[i_0_1606]) ).
cnf(i_0_2094,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1539]) ).
cnf(i_0_2095,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(scs_inference,[],[i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574]) ).
cnf(i_0_2096,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2097,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1574]) ).
cnf(i_0_2098,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(scs_inference,[],[i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581]) ).
cnf(i_0_2099,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1581]) ).
cnf(i_0_2100,plain,
~ c_member(X1,X2,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588]) ).
cnf(i_0_2101,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2102,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_member(X2,X3,X1) ),
inference(rename_variables,[],[i_0_1588]) ).
cnf(i_0_2103,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3)),
inference(scs_inference,[],[i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590]) ).
cnf(i_0_2104,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1590]) ).
cnf(i_0_2105,plain,
c_member(X1,esk17_2(hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632]) ).
cnf(i_0_2106,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1761]) ).
cnf(i_0_2107,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_member(X2,esk17_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_1632]) ).
cnf(i_0_2108,plain,
c_member(X1,esk16_2(hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633]) ).
cnf(i_0_2109,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1761]) ).
cnf(i_0_2110,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_member(X2,esk16_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_1633]) ).
cnf(i_0_2111,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635]) ).
cnf(i_0_2112,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1635]) ).
cnf(i_0_2113,plain,
c_member(X1,X2,c_Set_Oinsert(X3,X2,X4)),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641]) ).
cnf(i_0_2114,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_member(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1641]) ).
cnf(i_0_2115,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X1,tc_Nat_Onat,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660]) ).
cnf(i_0_2116,plain,
( c_member(tc_Nat_Onat,esk15_2(X1,X2),X1)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(rename_variables,[],[i_0_1660]) ).
cnf(i_0_2117,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661]) ).
cnf(i_0_2118,plain,
( c_member(tc_Nat_Onat,esk13_2(X1,X2),X1)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(rename_variables,[],[i_0_1661]) ).
cnf(i_0_2119,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664]) ).
cnf(i_0_2120,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2121,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1664]) ).
cnf(i_0_2122,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != X1,
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665]) ).
cnf(i_0_2123,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1761]) ).
cnf(i_0_2124,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
inference(rename_variables,[],[i_0_1665]) ).
cnf(i_0_2125,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680]) ).
cnf(i_0_2126,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2127,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(rename_variables,[],[i_0_1680]) ).
cnf(i_0_2128,plain,
~ class_Orderings_Otop(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1758,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714]) ).
cnf(i_0_2129,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X1),
inference(rename_variables,[],[i_0_1606]) ).
cnf(i_0_2130,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Orderings_Otop__class_Otop(X1))
| ~ class_Orderings_Otop(X1) ),
inference(rename_variables,[],[i_0_1714]) ).
cnf(i_0_2131,plain,
c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X1,X1),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1758,i_0_1796,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724]) ).
cnf(i_0_2132,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(rename_variables,[],[i_0_1724]) ).
cnf(i_0_2133,plain,
c_Finite__Set_Ocard(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1758,i_0_1796,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725]) ).
cnf(i_0_2134,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2135,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1725]) ).
cnf(i_0_2136,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1758,i_0_1796,i_0_1797,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760]) ).
cnf(i_0_2137,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2138,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1758,i_0_1796,i_0_1797,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121]) ).
cnf(i_0_2139,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1405]) ).
cnf(i_0_2140,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X2,X3,X5)
| X4 = X5 ),
inference(rename_variables,[],[i_0_1121]) ).
cnf(i_0_2141,plain,
c_Fun_Oinj__on(X1,X2,esk9_4(c_Set_Oinsert(X2,X3,X4),X2,X1,c_Set_Oinsert(X1,hAPP(X5,X3),c_Set_Oimage(X2,X1,X5,X4))),c_Set_Oinsert(X1,hAPP(X5,X3),c_Set_Oimage(X2,X1,X5,X4))),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1758,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129]) ).
cnf(i_0_2142,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1600]) ).
cnf(i_0_2143,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X3,X2,X4,X5) != X1
| c_Fun_Oinj__on(X2,X3,esk9_4(X5,X3,X2,X1),X1) ),
inference(rename_variables,[],[i_0_1129]) ).
cnf(i_0_2144,plain,
c_Fun_Oinj__on(X1,X2,X3,esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4,X1,c_Set_Oimage(X1,X5,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X5)),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1758,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174]) ).
cnf(i_0_2145,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Fun_Oinj__on(X1,X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
inference(rename_variables,[],[i_0_1174]) ).
cnf(i_0_2146,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1758,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400]) ).
cnf(i_0_2147,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_2148,plain,
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_1592]) ).
cnf(i_0_2149,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2)
| X2 = X3 ),
inference(rename_variables,[],[i_0_1400]) ).
cnf(i_0_2150,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1758,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496]) ).
cnf(i_0_2151,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(rename_variables,[],[i_0_1363]) ).
cnf(i_0_2152,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = X1 ),
inference(rename_variables,[],[i_0_1496]) ).
cnf(i_0_2153,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1736,i_0_1758,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573]) ).
cnf(i_0_2154,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_1736]) ).
cnf(i_0_2155,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1573]) ).
cnf(i_0_2156,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1961,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631]) ).
cnf(i_0_2157,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_1668]) ).
cnf(i_0_2158,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1631]) ).
cnf(i_0_2159,plain,
hAPP(c_Nat_OSuc,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(scs_inference,[],[i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807]) ).
cnf(i_0_2160,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1761]) ).
cnf(i_0_2161,plain,
c_member(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_fequal(X3))),
inference(scs_inference,[],[i_0_1996,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183]) ).
cnf(i_0_2162,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2163,plain,
( X1 != hAPP(X2,X3)
| c_member(X4,X1,c_Set_Oimage(X5,X4,X2,X6))
| ~ c_member(X5,X3,X6) ),
inference(rename_variables,[],[i_0_1183]) ).
cnf(i_0_2164,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(scs_inference,[],[i_0_1996,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478]) ).
cnf(i_0_2165,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_1464]) ).
cnf(i_0_2166,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != hAPP(c_Nat_OSuc,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_1478]) ).
cnf(i_0_2167,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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(scs_inference,[],[i_0_1996,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1788,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651]) ).
cnf(i_0_2168,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1651]) ).
cnf(i_0_2169,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1996,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1788,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653]) ).
cnf(i_0_2170,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1653]) ).
cnf(i_0_2171,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(scs_inference,[],[i_0_1996,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1788,i_0_1792,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654]) ).
cnf(i_0_2172,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1654]) ).
cnf(i_0_2173,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(scs_inference,[],[i_0_1996,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1788,i_0_1792,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655]) ).
cnf(i_0_2174,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1655]) ).
cnf(i_0_2175,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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(scs_inference,[],[i_0_1996,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1788,i_0_1792,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719]) ).
cnf(i_0_2176,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1719]) ).
cnf(i_0_2177,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1996,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720]) ).
cnf(i_0_2178,plain,
( ~ class_Orderings_Opreorder(X1)
| X2 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1720]) ).
cnf(i_0_2179,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(scs_inference,[],[i_0_1996,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721]) ).
cnf(i_0_2180,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1721]) ).
cnf(i_0_2181,plain,
X1 = esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),
inference(scs_inference,[],[i_0_1996,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940]) ).
cnf(i_0_2182,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1405]) ).
cnf(i_0_2183,plain,
c_member(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1177]) ).
cnf(i_0_2184,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_member(X2,hAPP(X3,X4),c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| X4 = esk4_4(hAPP(X3,X4),X3,X2,X1) ),
inference(rename_variables,[],[i_0_1940]) ).
cnf(i_0_2185,plain,
hAPP(c_fequal(X1),X1) != c_fFalse,
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892]) ).
cnf(i_0_2186,plain,
class_Orderings_Oorder(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894]) ).
cnf(i_0_2187,plain,
class_Orderings_Olinorder(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895]) ).
cnf(i_0_2188,plain,
class_Rings_Ocomm__semiring__1(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1777,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896]) ).
cnf(i_0_2189,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1777,i_0_1784,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897]) ).
cnf(i_0_2190,plain,
class_Groups_Oordered__ab__semigroup__add(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1777,i_0_1780,i_0_1784,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898]) ).
cnf(i_0_2191,plain,
class_Groups_Ocomm__monoid__add(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1777,i_0_1780,i_0_1782,i_0_1784,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900]) ).
cnf(i_0_2192,plain,
class_Groups_Oordered__comm__monoid__add(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1777,i_0_1779,i_0_1780,i_0_1782,i_0_1784,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904]) ).
cnf(i_0_2193,plain,
class_Rings_Olinordered__semidom(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1782,i_0_1784,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906]) ).
cnf(i_0_2194,plain,
class_Groups_Oab__semigroup__add(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1782,i_0_1784,i_0_1787,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908]) ).
cnf(i_0_2195,plain,
class_Orderings_Opreorder(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1782,i_0_1784,i_0_1787,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909]) ).
cnf(i_0_2196,plain,
class_Groups_Ocancel__semigroup__add(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1782,i_0_1784,i_0_1786,i_0_1787,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910]) ).
cnf(i_0_2197,plain,
class_Groups_Ocancel__ab__semigroup__add(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911]) ).
cnf(i_0_2198,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912]) ).
cnf(i_0_2199,plain,
class_Orderings_Oord(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913]) ).
cnf(i_0_2200,plain,
class_Orderings_Obot(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914]) ).
cnf(i_0_2201,plain,
tc_HOL_Obool != tc_Nat_Onat,
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915]) ).
cnf(i_0_2202,plain,
class_Groups_Omonoid__add(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917]) ).
cnf(i_0_2203,plain,
class_Rings_Ozero__neq__one(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918]) ).
cnf(i_0_2204,plain,
class_Groups_Oone(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919]) ).
cnf(i_0_2205,plain,
class_Groups_Ozero(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922]) ).
cnf(i_0_2206,plain,
~ c_member(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,c_Orderings_Obot__class_Obot(tc_fun(c_Set_Oimage(X3,X1,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923]) ).
cnf(i_0_2207,plain,
~ c_member(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rename_variables,[],[i_0_1520]) ).
cnf(i_0_2208,plain,
~ c_member(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X2,X1,c_Nat_OSuc,X3)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924]) ).
cnf(i_0_2209,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2210,plain,
~ c_member(tc_Nat_Onat,esk13_2(c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X1),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925]) ).
cnf(i_0_2211,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2212,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),X2,X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926]) ).
cnf(i_0_2213,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2214,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),c_Set_Oimage(X3,X2,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927]) ).
cnf(i_0_2215,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1976]) ).
cnf(i_0_2216,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928]) ).
cnf(i_0_2217,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1976]) ).
cnf(i_0_2218,plain,
~ c_Orderings_Oord__class_Oless__eq(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,X1),X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929]) ).
cnf(i_0_2219,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2220,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930]) ).
cnf(i_0_2221,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2222,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,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(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931]) ).
cnf(i_0_2223,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X1),
inference(rename_variables,[],[i_0_1606]) ).
cnf(i_0_2224,plain,
~ c_Finite__Set_Ofinite(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935]) ).
cnf(i_0_2225,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2226,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936]) ).
cnf(i_0_2227,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2228,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937]) ).
cnf(i_0_2229,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Nat_Onat),X2,X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089]) ).
cnf(i_0_2230,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1738]) ).
cnf(i_0_2231,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk6_4(X3,X2,X4,X1)),hAPP(X3,esk6_4(X3,X2,X4,X1)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ class_Orderings_Oord(X1) ),
inference(rename_variables,[],[i_0_1089]) ).
cnf(i_0_2232,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1600,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100]) ).
cnf(i_0_2233,plain,
c_member(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1177]) ).
cnf(i_0_2234,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1405]) ).
cnf(i_0_2235,plain,
( ~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))
| X2 = hAPP(X4,esk4_4(X2,X4,X1,X3))
| ~ c_Fun_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))) ),
inference(rename_variables,[],[i_0_1100]) ).
cnf(i_0_2236,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk9_4(c_Set_Oinsert(X1,X3,X4),X1,X2,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X1,X3,X4)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_1469,i_0_2026,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101]) ).
cnf(i_0_2237,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1600]) ).
cnf(i_0_2238,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oimage(X2,X3,esk9_4(X4,X3,X2,X1),X1),X4)
| c_Set_Oimage(X3,X2,X5,X4) != X1 ),
inference(rename_variables,[],[i_0_1101]) ).
cnf(i_0_2239,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Set_Oimage(X2,X1,X3,X4)),c_Set_Oimage(X2,X1,X3,c_Set_Oinsert(X2,X5,X4))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_1469,i_0_2026,i_0_2147,i_0_1692,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135]) ).
cnf(i_0_2240,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2241,plain,
( X1 != c_Set_Oimage(X2,X3,X4,X5)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oimage(X2,X3,X4,X6))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X5,X6) ),
inference(rename_variables,[],[i_0_1135]) ).
cnf(i_0_2242,plain,
c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_1469,i_0_2026,i_0_2147,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149]) ).
cnf(i_0_2243,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1692]) ).
cnf(i_0_2244,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X3,X1,X4,X5))
| c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X5) ),
inference(rename_variables,[],[i_0_1149]) ).
cnf(i_0_2245,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))),X3)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_1469,i_0_2026,i_0_2147,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220]) ).
cnf(i_0_2246,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1220]) ).
cnf(i_0_2247,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))),X3),X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_1469,i_0_2026,i_0_2147,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245]) ).
cnf(i_0_2248,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4) ),
inference(rename_variables,[],[i_0_1245]) ).
cnf(i_0_2249,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))),X3),X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246]) ).
cnf(i_0_2250,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1738]) ).
cnf(i_0_2251,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4) ),
inference(rename_variables,[],[i_0_1246]) ).
cnf(i_0_2252,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),hAPP(c_Nat_OSuc,X3))),X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283]) ).
cnf(i_0_2253,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1283]) ).
cnf(i_0_2254,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),hAPP(c_Nat_OSuc,X3))),X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287]) ).
cnf(i_0_2255,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1287]) ).
cnf(i_0_2256,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X3),X3),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327]) ).
cnf(i_0_2257,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1976]) ).
cnf(i_0_2258,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X4,X3) ),
inference(rename_variables,[],[i_0_1327]) ).
cnf(i_0_2259,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329]) ).
cnf(i_0_2260,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_2261,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X3) ),
inference(rename_variables,[],[i_0_1329]) ).
cnf(i_0_2262,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345]) ).
cnf(i_0_2263,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_2264,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1677]) ).
cnf(i_0_2265,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_1345]) ).
cnf(i_0_2266,plain,
c_member(X1,X2,c_Set_Oinsert(X1,X3,c_fequal(X2))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382]) ).
cnf(i_0_2267,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_2268,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X4,X2)
| c_member(X1,X4,X3) ),
inference(rename_variables,[],[i_0_1382]) ).
cnf(i_0_2269,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436]) ).
cnf(i_0_2270,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_1736]) ).
cnf(i_0_2271,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(rename_variables,[],[i_0_1436]) ).
cnf(i_0_2272,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(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(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_1364,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451]) ).
cnf(i_0_2273,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1761]) ).
cnf(i_0_2274,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(rename_variables,[],[i_0_1694]) ).
cnf(i_0_2275,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(X2,X1),X2) ),
inference(rename_variables,[],[i_0_1451]) ).
cnf(i_0_2276,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485]) ).
cnf(i_0_2277,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1485]) ).
cnf(i_0_2278,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486]) ).
cnf(i_0_2279,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1486]) ).
cnf(i_0_2280,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489]) ).
cnf(i_0_2281,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1489]) ).
cnf(i_0_2282,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493]) ).
cnf(i_0_2283,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1493]) ).
cnf(i_0_2284,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494]) ).
cnf(i_0_2285,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1494]) ).
cnf(i_0_2286,plain,
hAPP(c_Nat_OSuc,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505]) ).
cnf(i_0_2287,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| hAPP(c_Nat_OSuc,X1) = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1505]) ).
cnf(i_0_2288,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oinsert(tc_Nat_Onat,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541]) ).
cnf(i_0_2289,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_2290,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(rename_variables,[],[i_0_1541]) ).
cnf(i_0_2291,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556]) ).
cnf(i_0_2292,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1556]) ).
cnf(i_0_2293,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558]) ).
cnf(i_0_2294,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2295,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Product__Type_Ounit,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583]) ).
cnf(i_0_2296,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1761]) ).
cnf(i_0_2297,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_1583]) ).
cnf(i_0_2298,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618]) ).
cnf(i_0_2299,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1618]) ).
cnf(i_0_2300,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620]) ).
cnf(i_0_2301,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1620]) ).
cnf(i_0_2302,plain,
c_Finite__Set_Ocard(tc_Product__Type_Ounit,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693]) ).
cnf(i_0_2303,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1761]) ).
cnf(i_0_2304,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_1693]) ).
cnf(i_0_2305,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702]) ).
cnf(i_0_2306,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2307,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(rename_variables,[],[i_0_1702]) ).
cnf(i_0_2308,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,esk8_4(c_Set_Oinsert(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Set_Oinsert(tc_Nat_Onat,X2,X3))),tc_Nat_Onat,tc_Nat_Onat,c_Set_Oinsert(tc_Nat_Onat,X2,X3)),c_Set_Oinsert(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Set_Oinsert(tc_Nat_Onat,X2,X3)))) = c_Set_Oinsert(tc_Nat_Onat,X2,X3),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099]) ).
cnf(i_0_2309,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1600]) ).
cnf(i_0_2310,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_2311,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1405]) ).
cnf(i_0_2312,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X3,X2,esk8_4(X4,X3,X2,X1),X4) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oimage(X2,X3,X5,X1),X4)
| ~ c_Fun_Oinj__on(X2,X3,X5,X1) ),
inference(rename_variables,[],[i_0_1099]) ).
cnf(i_0_2313,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477]) ).
cnf(i_0_2314,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_1542]) ).
cnf(i_0_2315,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1477]) ).
cnf(i_0_2316,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604]) ).
cnf(i_0_2317,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(rename_variables,[],[i_0_1397]) ).
cnf(i_0_2318,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_2319,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1604]) ).
cnf(i_0_2320,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X3))),X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236]) ).
cnf(i_0_2321,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1236]) ).
cnf(i_0_2322,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237]) ).
cnf(i_0_2323,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(rename_variables,[],[i_0_1398]) ).
cnf(i_0_2324,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1237]) ).
cnf(i_0_2325,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),hAPP(c_Nat_OSuc,X3)),X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238]) ).
cnf(i_0_2326,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1238]) ).
cnf(i_0_2327,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274]) ).
cnf(i_0_2328,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1274]) ).
cnf(i_0_2329,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276]) ).
cnf(i_0_2330,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1276]) ).
cnf(i_0_2331,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))),X2),X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299]) ).
cnf(i_0_2332,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1677]) ).
cnf(i_0_2333,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1299]) ).
cnf(i_0_2334,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356]) ).
cnf(i_0_2335,plain,
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(rename_variables,[],[i_0_1591]) ).
cnf(i_0_2336,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X4,X3)
| ~ class_Orderings_Oord(X2) ),
inference(rename_variables,[],[i_0_1356]) ).
cnf(i_0_2337,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450]) ).
cnf(i_0_2338,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_1736]) ).
cnf(i_0_2339,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1450]) ).
cnf(i_0_2340,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368]) ).
cnf(i_0_2341,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2342,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2343,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_1736]) ).
cnf(i_0_2344,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(rename_variables,[],[i_0_1368]) ).
cnf(i_0_2345,plain,
c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,X3,c_Orderings_Obot__class_Obot(tc_fun(c_Set_Oimage(X4,X1,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170]) ).
cnf(i_0_2346,plain,
( c_member(X1,esk3_4(X2,X3,X4,X1),X2)
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(rename_variables,[],[i_0_1170]) ).
cnf(i_0_2347,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(c_Nat_OSuc,X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178]) ).
cnf(i_0_2348,plain,
( c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))
| X2 != hAPP(X4,X5) ),
inference(rename_variables,[],[i_0_1178]) ).
cnf(i_0_2349,plain,
hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))) != hAPP(c_Nat_OSuc,X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734]) ).
cnf(i_0_2350,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_1734]) ).
cnf(i_0_2351,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270]) ).
cnf(i_0_2352,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2),X3) ),
inference(rename_variables,[],[i_0_1270]) ).
cnf(i_0_2353,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444]) ).
cnf(i_0_2354,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1444]) ).
cnf(i_0_2355,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X1),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472]) ).
cnf(i_0_2356,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1472]) ).
cnf(i_0_2357,plain,
esk23_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585]) ).
cnf(i_0_2358,plain,
( ~ 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(rename_variables,[],[i_0_1585]) ).
cnf(i_0_2359,plain,
( hAPP(c_Nat_OSuc,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),hAPP(c_Nat_OSuc,X1)) ),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585,i_0_1445]) ).
cnf(i_0_2360,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(rename_variables,[],[i_0_1363]) ).
cnf(i_0_2361,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1445]) ).
cnf(i_0_2362,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_2314,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585,i_0_1445,i_0_1515]) ).
cnf(i_0_2363,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_1542]) ).
cnf(i_0_2364,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1515]) ).
cnf(i_0_2365,plain,
class_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_2314,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585,i_0_1445,i_0_1515,i_0_1916]) ).
cnf(i_0_2366,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X2),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_2314,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585,i_0_1445,i_0_1515,i_0_1916,i_0_1401]) ).
cnf(i_0_2367,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1401]) ).
cnf(i_0_2368,plain,
c_member(tc_Product__Type_Ounit,esk42_2(hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))),tc_Product__Type_Ounit),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_2314,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585,i_0_1445,i_0_1515,i_0_1916,i_0_1401,i_0_1605]) ).
cnf(i_0_2369,plain,
( c_Finite__Set_Ocard(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_member(X1,esk42_2(X2,X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1605]) ).
cnf(i_0_2370,plain,
( c_Set_Oinsert(X1,X2,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_2314,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585,i_0_1445,i_0_1515,i_0_1916,i_0_1401,i_0_1605,i_0_1453]) ).
cnf(i_0_2371,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 = X3 ),
inference(rename_variables,[],[i_0_1453]) ).
cnf(i_0_2372,plain,
( hAPP(c_Nat_OSuc,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) ),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_2314,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585,i_0_1445,i_0_1515,i_0_1916,i_0_1401,i_0_1605,i_0_1453,i_0_1498]) ).
cnf(i_0_2373,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(rename_variables,[],[i_0_1364]) ).
cnf(i_0_2374,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1498]) ).
cnf(i_0_2375,plain,
( c_Arrow__Order__Mirabelle_Ounanimity(X1)
| v_F != X1 ),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_2314,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1799,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585,i_0_1445,i_0_1515,i_0_1916,i_0_1401,i_0_1605,i_0_1453,i_0_1498,i_0_1920]) ).
cnf(i_0_2376,plain,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| v_F != X1 ),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_2314,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1799,i_0_1800,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585,i_0_1445,i_0_1515,i_0_1916,i_0_1401,i_0_1605,i_0_1453,i_0_1498,i_0_1920,i_0_1921]) ).
cnf(i_0_2377,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(scs_inference,[],[i_0_1996,i_0_2000,i_0_1961,i_0_1976,i_0_2215,i_0_2217,i_0_1957,i_0_1677,i_0_2088,i_0_2264,i_0_1738,i_0_2083,i_0_2230,i_0_2250,i_0_1469,i_0_2026,i_0_2147,i_0_2260,i_0_2267,i_0_2289,i_0_1692,i_0_2015,i_0_1967,i_0_1353,i_0_1761,i_0_2061,i_0_2106,i_0_2109,i_0_2123,i_0_2160,i_0_2273,i_0_2296,i_0_2303,i_0_1768,i_0_2029,i_0_2032,i_0_2058,i_0_2074,i_0_2096,i_0_2101,i_0_2120,i_0_2126,i_0_2134,i_0_2162,i_0_2209,i_0_2211,i_0_2213,i_0_2219,i_0_2221,i_0_2225,i_0_2227,i_0_2240,i_0_2306,i_0_1520,i_0_2018,i_0_1397,i_0_2009,i_0_2046,i_0_2049,i_0_1398,i_0_1542,i_0_2038,i_0_2041,i_0_2067,i_0_2314,i_0_1543,i_0_1405,i_0_2139,i_0_2182,i_0_2234,i_0_1606,i_0_2052,i_0_2055,i_0_2093,i_0_2129,i_0_2223,i_0_1694,i_0_2077,i_0_2274,i_0_1591,i_0_1592,i_0_1668,i_0_1736,i_0_2154,i_0_2270,i_0_2338,i_0_1758,i_0_1690,i_0_1773,i_0_1774,i_0_1775,i_0_1776,i_0_1777,i_0_1778,i_0_1779,i_0_1780,i_0_1781,i_0_1782,i_0_1783,i_0_1784,i_0_1785,i_0_1786,i_0_1787,i_0_1788,i_0_1790,i_0_1791,i_0_1792,i_0_1793,i_0_1795,i_0_1796,i_0_1797,i_0_1799,i_0_1800,i_0_1801,i_0_1802,i_0_1152,i_0_1177,i_0_2183,i_0_1717,i_0_1600,i_0_2142,i_0_2237,i_0_1363,i_0_2064,i_0_2151,i_0_1364,i_0_2035,i_0_1730,i_0_2263,i_0_1464,i_0_1659,i_0_1806,i_0_1673,i_0_1674,i_0_1689,i_0_1691,i_0_1825,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1302,i_0_1332,i_0_1333,i_0_1348,i_0_1351,i_0_1352,i_0_1388,i_0_1410,i_0_1412,i_0_1414,i_0_1416,i_0_1417,i_0_1429,i_0_1443,i_0_1447,i_0_1448,i_0_1473,i_0_1506,i_0_1507,i_0_1510,i_0_1511,i_0_1512,i_0_1535,i_0_1537,i_0_1539,i_0_1574,i_0_1581,i_0_1588,i_0_1590,i_0_1632,i_0_1633,i_0_1635,i_0_1641,i_0_1660,i_0_1661,i_0_1664,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1725,i_0_1760,i_0_1121,i_0_1129,i_0_1174,i_0_1400,i_0_1496,i_0_1573,i_0_1631,i_0_1807,i_0_1183,i_0_1478,i_0_1651,i_0_1653,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1940,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1936,i_0_1937,i_0_1089,i_0_1100,i_0_1101,i_0_1135,i_0_1149,i_0_1220,i_0_1245,i_0_1246,i_0_1283,i_0_1287,i_0_1327,i_0_1329,i_0_1345,i_0_1382,i_0_1436,i_0_1451,i_0_1485,i_0_1486,i_0_1489,i_0_1493,i_0_1494,i_0_1505,i_0_1541,i_0_1556,i_0_1558,i_0_1583,i_0_1618,i_0_1620,i_0_1693,i_0_1702,i_0_1099,i_0_1477,i_0_1604,i_0_1236,i_0_1237,i_0_1238,i_0_1274,i_0_1276,i_0_1299,i_0_1356,i_0_1450,i_0_1368,i_0_1170,i_0_1178,i_0_1734,i_0_1270,i_0_1444,i_0_1472,i_0_1585,i_0_1445,i_0_1515,i_0_1916,i_0_1401,i_0_1605,i_0_1453,i_0_1498,i_0_1920,i_0_1921,i_0_1197]) ).
cnf(i_0_2378,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1761]) ).
cnf(i_0_2379,plain,
( X1 = c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_2380,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(equality_inference,[],[2375]) ).
cnf(i_0_2381,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(equality_inference,[],[2376]) ).
cnf(i_0_2382,plain,
c_Arrow__Order__Mirabelle_Ounanimity(c_Nat_Osize__class_Osize(tc_Nat_Onat,v_F)),
inference(scs_inference,[],[i_0_2003,i_0_2375]) ).
cnf(i_0_2383,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2384,plain,
c_Arrow__Order__Mirabelle_OIIA(c_Nat_Osize__class_Osize(tc_Nat_Onat,v_F)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2375,i_0_2376]) ).
cnf(i_0_2385,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2386,plain,
c_Fun_Oinj__on(X1,X2,X3,c_Set_Oimage(X4,X1,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2017,i_0_2375,i_0_2376,i_0_1171]) ).
cnf(i_0_2387,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_2017]) ).
cnf(i_0_2388,plain,
( c_member(X1,esk2_4(X2,X3,X4,X1),X2)
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(rename_variables,[],[i_0_1171]) ).
cnf(i_0_2389,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3),X1),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2164,i_0_2017,i_0_2375,i_0_2376,i_0_1171,i_0_1303]) ).
cnf(i_0_2390,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2164]) ).
cnf(i_0_2391,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1303]) ).
cnf(i_0_2392,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3),X1),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2164,i_0_2017,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305]) ).
cnf(i_0_2393,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2090]) ).
cnf(i_0_2394,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1305]) ).
cnf(i_0_2395,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,esk19_5(c_Set_Oimage(X1,X4,X3,X2),X5,X4,c_Set_Oimage(X4,X6,X5,c_Set_Oimage(X1,X4,X3,X2)),X6),X4),X2),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2164,i_0_2017,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088]) ).
cnf(i_0_2396,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,c_Set_Oimage(X1,X4,X3,X2),X4),X2),
inference(rename_variables,[],[i_0_2014]) ).
cnf(i_0_2397,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X3,X1,X4,X5))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),esk19_5(X5,X4,X3,X2,X1),X5) ),
inference(rename_variables,[],[i_0_1088]) ).
cnf(i_0_2398,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Set_Oimage(X5,X3,X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2164,i_0_2017,i_0_2387,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114]) ).
cnf(i_0_2399,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_2017]) ).
cnf(i_0_2400,plain,
( c_member(X1,esk18_4(X2,X3,X1,X4),X2)
| ~ c_member(X5,X4,c_Set_Oimage(X1,X5,X3,X2)) ),
inference(rename_variables,[],[i_0_1114]) ).
cnf(i_0_2401,plain,
~ c_member(X1,c_Finite__Set_Ocard(X2,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),c_Set_Oimage(X3,X1,c_Nat_OSuc,X4)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2011,i_0_2164,i_0_2017,i_0_2387,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115]) ).
cnf(i_0_2402,plain,
c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,X2),
inference(rename_variables,[],[i_0_2011]) ).
cnf(i_0_2403,plain,
( X1 = hAPP(X2,esk18_4(X3,X2,X4,X1))
| ~ c_member(X5,X1,c_Set_Oimage(X4,X5,X2,X3)) ),
inference(rename_variables,[],[i_0_1115]) ).
cnf(i_0_2404,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,c_Set_Oimage(X4,X2,esk9_4(c_Set_Oinsert(X2,X5,X6),X2,X4,c_Set_Oinsert(X4,hAPP(X7,X5),c_Set_Oimage(X2,X4,X7,X6))),c_Set_Oinsert(X4,hAPP(X7,X5),c_Set_Oimage(X2,X4,X7,X6)))),c_Set_Oimage(X2,X1,X3,c_Set_Oinsert(X2,X5,X6))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2011,i_0_2164,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125]) ).
cnf(i_0_2405,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2),c_Set_Oimage(X1,X4,X5,X3)) ),
inference(rename_variables,[],[i_0_1125]) ).
cnf(i_0_2406,plain,
~ c_member(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2011,i_0_2164,i_0_1731,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588]) ).
cnf(i_0_2407,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2408,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_member(X2,X3,X1) ),
inference(rename_variables,[],[i_0_1588]) ).
cnf(i_0_2409,plain,
c_member(X1,esk17_2(hAPP(c_Nat_OSuc,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X1),hAPP(c_Nat_OSuc,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2164,i_0_1731,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632]) ).
cnf(i_0_2410,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_member(X2,esk17_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_1632]) ).
cnf(i_0_2411,plain,
c_member(X1,esk16_2(hAPP(c_Nat_OSuc,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X1),hAPP(c_Nat_OSuc,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2164,i_0_1731,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633]) ).
cnf(i_0_2412,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_member(X2,esk16_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_1633]) ).
cnf(i_0_2413,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2164,i_0_1731,i_0_2407,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680]) ).
cnf(i_0_2414,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2415,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(rename_variables,[],[i_0_1680]) ).
cnf(i_0_2416,plain,
~ class_Orderings_Otop(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2218,i_0_2164,i_0_1731,i_0_2407,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714]) ).
cnf(i_0_2417,plain,
~ c_Orderings_Oord__class_Oless__eq(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,X1),X1),
inference(rename_variables,[],[i_0_2218]) ).
cnf(i_0_2418,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Orderings_Otop__class_Otop(X1))
| ~ class_Orderings_Otop(X1) ),
inference(rename_variables,[],[i_0_1714]) ).
cnf(i_0_2419,plain,
c_Finite__Set_Ocard(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2218,i_0_2164,i_0_1731,i_0_2407,i_0_2414,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725]) ).
cnf(i_0_2420,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2421,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1725]) ).
cnf(i_0_2422,plain,
c_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_1731,i_0_2407,i_0_2414,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760]) ).
cnf(i_0_2423,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2424,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(c_Nat_OSuc,X1),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_1731,i_0_2407,i_0_2414,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691]) ).
cnf(i_0_2425,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_2262]) ).
cnf(i_0_2426,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(rename_variables,[],[i_0_1691]) ).
cnf(i_0_2427,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332]) ).
cnf(i_0_2428,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2429,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = c_Set_Oimage(X2,X3,X4,X1) ),
inference(rename_variables,[],[i_0_1332]) ).
cnf(i_0_2430,plain,
c_Set_Oimage(X1,X2,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333]) ).
cnf(i_0_2431,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2432,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X2,X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_1333]) ).
cnf(i_0_2433,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3),X4),X1),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410]) ).
cnf(i_0_2434,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2164]) ).
cnf(i_0_2435,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1410]) ).
cnf(i_0_2436,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417]) ).
cnf(i_0_2437,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2438,plain,
( X1 != hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1417]) ).
cnf(i_0_2439,plain,
c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641]) ).
cnf(i_0_2440,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_member(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1641]) ).
cnf(i_0_2441,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X1,tc_Nat_Onat,X2,c_Set_Oimage(X3,X1,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661]) ).
cnf(i_0_2442,plain,
( c_member(tc_Nat_Onat,esk13_2(X1,X2),X1)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(rename_variables,[],[i_0_1661]) ).
cnf(i_0_2443,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) != X1,
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665]) ).
cnf(i_0_2444,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) != X1,
inference(rename_variables,[],[i_0_2008]) ).
cnf(i_0_2445,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
inference(rename_variables,[],[i_0_1665]) ).
cnf(i_0_2446,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1,X1),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724]) ).
cnf(i_0_2447,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(rename_variables,[],[i_0_1724]) ).
cnf(i_0_2448,plain,
c_Fun_Oinj__on(X1,X2,X3,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170]) ).
cnf(i_0_2449,plain,
~ c_member(X1,X2,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_2100]) ).
cnf(i_0_2450,plain,
( c_member(X1,esk3_4(X2,X3,X4,X1),X2)
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(rename_variables,[],[i_0_1170]) ).
cnf(i_0_2451,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673]) ).
cnf(i_0_2452,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_1673]) ).
cnf(i_0_2453,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != esk23_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674]) ).
cnf(i_0_2454,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(rename_variables,[],[i_0_1674]) ).
cnf(i_0_2455,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348]) ).
cnf(i_0_2456,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2150]) ).
cnf(i_0_2457,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1348]) ).
cnf(i_0_2458,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3),X4),X2),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412]) ).
cnf(i_0_2459,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2164]) ).
cnf(i_0_2460,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1412]) ).
cnf(i_0_2461,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X2),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2220,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2262,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416]) ).
cnf(i_0_2462,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1),
inference(rename_variables,[],[i_0_2220]) ).
cnf(i_0_2463,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1416]) ).
cnf(i_0_2464,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X3))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2220,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443]) ).
cnf(i_0_2465,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))),
inference(rename_variables,[],[i_0_2034]) ).
cnf(i_0_2466,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1443]) ).
cnf(i_0_2467,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2220,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506]) ).
cnf(i_0_2468,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2469,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1)) ),
inference(rename_variables,[],[i_0_1506]) ).
cnf(i_0_2470,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X3)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2220,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507]) ).
cnf(i_0_2471,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3)),
inference(rename_variables,[],[i_0_2103]) ).
cnf(i_0_2472,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1507]) ).
cnf(i_0_2473,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635]) ).
cnf(i_0_2474,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1635]) ).
cnf(i_0_2475,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664]) ).
cnf(i_0_2476,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2477,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1664]) ).
cnf(i_0_2478,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)) != X1,
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734]) ).
cnf(i_0_2479,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_1734]) ).
cnf(i_0_2480,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414]) ).
cnf(i_0_2481,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(rename_variables,[],[i_0_2313]) ).
cnf(i_0_2482,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1414]) ).
cnf(i_0_2483,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Nat_OSuc,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429]) ).
cnf(i_0_2484,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
inference(rename_variables,[],[i_0_1429]) ).
cnf(i_0_2485,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X3),X1),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535]) ).
cnf(i_0_2486,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2164]) ).
cnf(i_0_2487,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1535]) ).
cnf(i_0_2488,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X1),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539]) ).
cnf(i_0_2489,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1),
inference(rename_variables,[],[i_0_2220]) ).
cnf(i_0_2490,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1539]) ).
cnf(i_0_2491,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574]) ).
cnf(i_0_2492,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1574]) ).
cnf(i_0_2493,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590]) ).
cnf(i_0_2494,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(rename_variables,[],[i_0_2171]) ).
cnf(i_0_2495,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1590]) ).
cnf(i_0_2496,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660]) ).
cnf(i_0_2497,plain,
( c_member(tc_Nat_Onat,esk15_2(X1,X2),X1)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(rename_variables,[],[i_0_1660]) ).
cnf(i_0_2498,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X4,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270]) ).
cnf(i_0_2499,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2),X3) ),
inference(rename_variables,[],[i_0_1270]) ).
cnf(i_0_2500,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2040,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447]) ).
cnf(i_0_2501,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3)),
inference(rename_variables,[],[i_0_2040]) ).
cnf(i_0_2502,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1447]) ).
cnf(i_0_2503,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X3) != X1,
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2040,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689]) ).
cnf(i_0_2504,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2164]) ).
cnf(i_0_2505,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1689]) ).
cnf(i_0_2506,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X4)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2040,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351]) ).
cnf(i_0_2507,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),
inference(rename_variables,[],[i_0_2037]) ).
cnf(i_0_2508,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1351]) ).
cnf(i_0_2509,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3),X4)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2040,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352]) ).
cnf(i_0_2510,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),
inference(rename_variables,[],[i_0_2037]) ).
cnf(i_0_2511,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1352]) ).
cnf(i_0_2512,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)),X3)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510]) ).
cnf(i_0_2513,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3)),
inference(rename_variables,[],[i_0_2040]) ).
cnf(i_0_2514,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1510]) ).
cnf(i_0_2515,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X3),X1),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537]) ).
cnf(i_0_2516,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2164]) ).
cnf(i_0_2517,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1537]) ).
cnf(i_0_2518,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk23_2(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(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581]) ).
cnf(i_0_2519,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1581]) ).
cnf(i_0_2520,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3)),X2),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2284,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473]) ).
cnf(i_0_2521,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X2),
inference(rename_variables,[],[i_0_2284]) ).
cnf(i_0_2522,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1473]) ).
cnf(i_0_2523,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2284,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511]) ).
cnf(i_0_2524,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),
inference(rename_variables,[],[i_0_2037]) ).
cnf(i_0_2525,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1511]) ).
cnf(i_0_2526,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X3))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2284,i_0_2293,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444]) ).
cnf(i_0_2527,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))),
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_2528,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1444]) ).
cnf(i_0_2529,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),esk23_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2284,i_0_2293,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448]) ).
cnf(i_0_2530,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1448]) ).
cnf(i_0_2531,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3)),X2),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472]) ).
cnf(i_0_2532,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X2),
inference(rename_variables,[],[i_0_2282]) ).
cnf(i_0_2533,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1472]) ).
cnf(i_0_2534,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk23_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512]) ).
cnf(i_0_2535,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1512]) ).
cnf(i_0_2536,plain,
c_Set_Oinsert(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_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806]) ).
cnf(i_0_2537,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) != X2,
inference(scs_inference,[],[i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825]) ).
cnf(i_0_2538,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),X3)),
inference(scs_inference,[],[i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_1784,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222]) ).
cnf(i_0_2539,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1222]) ).
cnf(i_0_2540,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)),
inference(scs_inference,[],[i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_1784,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282]) ).
cnf(i_0_2541,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(rename_variables,[],[i_0_2173]) ).
cnf(i_0_2542,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(rename_variables,[],[i_0_1282]) ).
cnf(i_0_2543,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3),X2),
inference(scs_inference,[],[i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_1784,i_0_1780,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289]) ).
cnf(i_0_2544,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1289]) ).
cnf(i_0_2545,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_1784,i_0_1780,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644]) ).
cnf(i_0_2546,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2547,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = 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))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1644]) ).
cnf(i_0_2548,plain,
c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1784,i_0_1780,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124]) ).
cnf(i_0_2549,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(rename_variables,[],[i_0_2136]) ).
cnf(i_0_2550,plain,
c_Fun_Oinj__on(X1,X2,esk9_4(c_Set_Oinsert(X2,X3,X4),X2,X1,c_Set_Oinsert(X1,hAPP(X5,X3),c_Set_Oimage(X2,X1,X5,X4))),c_Set_Oinsert(X1,hAPP(X5,X3),c_Set_Oimage(X2,X1,X5,X4))),
inference(rename_variables,[],[i_0_2141]) ).
cnf(i_0_2551,plain,
( ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,X4))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4)
| c_Finite__Set_Ofinite(X2,X4) ),
inference(rename_variables,[],[i_0_1124]) ).
cnf(i_0_2552,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),X3)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1784,i_0_1780,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226]) ).
cnf(i_0_2553,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1226]) ).
cnf(i_0_2554,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3),X2),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285]) ).
cnf(i_0_2555,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1285]) ).
cnf(i_0_2556,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),X1),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288]) ).
cnf(i_0_2557,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_1288]) ).
cnf(i_0_2558,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X4)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224]) ).
cnf(i_0_2559,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1224]) ).
cnf(i_0_2560,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),X1),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284]) ).
cnf(i_0_2561,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_1284]) ).
cnf(i_0_2562,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X5,X1,c_Set_Oimage(X1,X6,X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X6)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328]) ).
cnf(i_0_2563,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),
inference(rename_variables,[],[i_0_2216]) ).
cnf(i_0_2564,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,c_Set_Oimage(X1,X4,X3,X2),X4),X2),
inference(rename_variables,[],[i_0_2014]) ).
cnf(i_0_2565,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X3) ),
inference(rename_variables,[],[i_0_1328]) ).
cnf(i_0_2566,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,esk9_4(c_Set_Oinsert(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Set_Oinsert(tc_Nat_Onat,X2,X3))),tc_Nat_Onat,tc_Nat_Onat,c_Set_Oinsert(tc_Nat_Onat,X2,X3)),c_Set_Oinsert(tc_Nat_Onat,X2,X3)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1600,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129]) ).
cnf(i_0_2567,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1600]) ).
cnf(i_0_2568,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X3,X2,X4,X5) != X1
| c_Fun_Oinj__on(X2,X3,esk9_4(X5,X3,X2,X1),X1) ),
inference(rename_variables,[],[i_0_1129]) ).
cnf(i_0_2569,plain,
esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,X1,c_Set_Oimage(X1,X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1591,i_0_1600,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400]) ).
cnf(i_0_2570,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,c_Set_Oimage(X1,X4,X3,X2),X4),X2),
inference(rename_variables,[],[i_0_2014]) ).
cnf(i_0_2571,plain,
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(rename_variables,[],[i_0_1591]) ).
cnf(i_0_2572,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2)
| X2 = X3 ),
inference(rename_variables,[],[i_0_1400]) ).
cnf(i_0_2573,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2150,i_0_2313,i_0_2195,i_0_2008,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1542,i_0_1591,i_0_1600,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573]) ).
cnf(i_0_2574,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_2262]) ).
cnf(i_0_2575,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_1542]) ).
cnf(i_0_2576,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1573]) ).
cnf(i_0_2577,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),X2,X2),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1542,i_0_1591,i_0_1600,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089]) ).
cnf(i_0_2578,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk6_4(X3,X2,X4,X1)),hAPP(X3,esk6_4(X3,X2,X4,X1)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ class_Orderings_Oord(X1) ),
inference(rename_variables,[],[i_0_1089]) ).
cnf(i_0_2579,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,esk9_4(c_Set_Oinsert(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Set_Oinsert(tc_Nat_Onat,X2,X3))),tc_Nat_Onat,tc_Nat_Onat,c_Set_Oinsert(tc_Nat_Onat,X2,X3)),c_Set_Oinsert(tc_Nat_Onat,X2,X3)),c_Set_Oinsert(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Set_Oinsert(tc_Nat_Onat,X2,X3)))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1542,i_0_1591,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101]) ).
cnf(i_0_2580,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1600]) ).
cnf(i_0_2581,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oimage(X2,X3,esk9_4(X4,X3,X2,X1),X1),X4)
| c_Set_Oimage(X3,X2,X5,X4) != X1 ),
inference(rename_variables,[],[i_0_1101]) ).
cnf(i_0_2582,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_1542,i_0_1591,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197]) ).
cnf(i_0_2583,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) != X1,
inference(rename_variables,[],[i_0_2008]) ).
cnf(i_0_2584,plain,
( X1 = c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_2585,plain,
c_Finite__Set_Ocard(tc_Product__Type_Ounit,hAPP(c_Nat_OSuc,c_Set_Oimage(X1,tc_Product__Type_Ounit,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1591,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693]) ).
cnf(i_0_2586,plain,
hAPP(c_Nat_OSuc,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(rename_variables,[],[i_0_2159]) ).
cnf(i_0_2587,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(rename_variables,[],[i_0_2136]) ).
cnf(i_0_2588,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_1693]) ).
cnf(i_0_2589,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) != c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1405,i_0_1591,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121]) ).
cnf(i_0_2590,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1405]) ).
cnf(i_0_2591,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X2,X3,X5)
| X4 = X5 ),
inference(rename_variables,[],[i_0_1121]) ).
cnf(i_0_2592,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk23_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496]) ).
cnf(i_0_2593,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_1668]) ).
cnf(i_0_2594,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = X1 ),
inference(rename_variables,[],[i_0_1496]) ).
cnf(i_0_2595,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Set_Oinsert(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_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651]) ).
cnf(i_0_2596,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1651]) ).
cnf(i_0_2597,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653]) ).
cnf(i_0_2598,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1653]) ).
cnf(i_0_2599,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X2,X1,X3,c_Set_Oimage(X4,X2,esk9_4(c_Set_Oinsert(X2,X5,X6),X2,X4,c_Set_Oinsert(X4,hAPP(X7,X5),c_Set_Oimage(X2,X4,X7,X6))),c_Set_Oinsert(X4,hAPP(X7,X5),c_Set_Oimage(X2,X4,X7,X6)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X2,X1,X3,c_Set_Oinsert(X2,X5,X6))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135]) ).
cnf(i_0_2600,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2601,plain,
( X1 != c_Set_Oimage(X2,X3,X4,X5)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oimage(X2,X3,X4,X6))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X5,X6) ),
inference(rename_variables,[],[i_0_1135]) ).
cnf(i_0_2602,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220]) ).
cnf(i_0_2603,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3)),
inference(rename_variables,[],[i_0_2103]) ).
cnf(i_0_2604,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1220]) ).
cnf(i_0_2605,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X3),c_Set_Oimage(X4,X1,esk9_4(c_Set_Oinsert(X1,X2,X3),X1,X4,c_Set_Oinsert(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3))),c_Set_Oinsert(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3)))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327]) ).
cnf(i_0_2606,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1976]) ).
cnf(i_0_2607,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X4,X3) ),
inference(rename_variables,[],[i_0_1327]) ).
cnf(i_0_2608,plain,
~ c_member(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk19_5(c_Set_Oimage(X2,X1,c_Nat_OSuc,X3),X4,X1,c_Set_Oimage(X1,X5,X4,c_Set_Oimage(X2,X1,c_Nat_OSuc,X3)),X5)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382]) ).
cnf(i_0_2609,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,c_Set_Oimage(X1,X4,X3,X2),X4),X2),
inference(rename_variables,[],[i_0_2014]) ).
cnf(i_0_2610,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X4,X2)
| c_member(X1,X4,X3) ),
inference(rename_variables,[],[i_0_1382]) ).
cnf(i_0_2611,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3)),hAPP(c_Nat_OSuc,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451]) ).
cnf(i_0_2612,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))),
inference(rename_variables,[],[i_0_2034]) ).
cnf(i_0_2613,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(X2,X1),X2) ),
inference(rename_variables,[],[i_0_1451]) ).
cnf(i_0_2614,plain,
c_Finite__Set_Ofinite(X1,esk19_5(c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X4,X1,c_Set_Oimage(X1,X5,X4,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X5)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541]) ).
cnf(i_0_2615,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,c_Set_Oimage(X1,X4,X3,X2),X4),X2),
inference(rename_variables,[],[i_0_2014]) ).
cnf(i_0_2616,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(rename_variables,[],[i_0_1541]) ).
cnf(i_0_2617,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Product__Type_Ounit,hAPP(c_Nat_OSuc,c_Set_Oimage(X1,tc_Product__Type_Ounit,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583]) ).
cnf(i_0_2618,plain,
hAPP(c_Nat_OSuc,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(rename_variables,[],[i_0_2159]) ).
cnf(i_0_2619,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(rename_variables,[],[i_0_2136]) ).
cnf(i_0_2620,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_1583]) ).
cnf(i_0_2621,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654]) ).
cnf(i_0_2622,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1654]) ).
cnf(i_0_2623,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655]) ).
cnf(i_0_2624,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1655]) ).
cnf(i_0_2625,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Set_Oinsert(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_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719]) ).
cnf(i_0_2626,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1719]) ).
cnf(i_0_2627,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720]) ).
cnf(i_0_2628,plain,
( ~ class_Orderings_Opreorder(X1)
| X2 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1720]) ).
cnf(i_0_2629,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721]) ).
cnf(i_0_2630,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1721]) ).
cnf(i_0_2631,plain,
c_Finite__Set_Ofinite(X1,c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X3)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149]) ).
cnf(i_0_2632,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X3,c_Set_Oinsert(X2,X5,X4))),
inference(rename_variables,[],[i_0_2023]) ).
cnf(i_0_2633,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(rename_variables,[],[i_0_2136]) ).
cnf(i_0_2634,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X3,X1,X4,X5))
| c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X5) ),
inference(rename_variables,[],[i_0_1149]) ).
cnf(i_0_2635,plain,
X1 = c_Groups_Oplus__class_Oplus(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702]) ).
cnf(i_0_2636,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2637,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(rename_variables,[],[i_0_1702]) ).
cnf(i_0_2638,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1730,i_0_1784,i_0_1780,i_0_1783,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345]) ).
cnf(i_0_2639,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_2640,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(rename_variables,[],[i_0_2173]) ).
cnf(i_0_2641,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_1345]) ).
cnf(i_0_2642,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk23_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1730,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486]) ).
cnf(i_0_2643,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1486]) ).
cnf(i_0_2644,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))),X3)),
inference(scs_inference,[],[i_0_2141,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1730,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556]) ).
cnf(i_0_2645,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1556]) ).
cnf(i_0_2646,plain,
c_Fun_Oinj__on(X1,X2,esk9_4(c_Set_Oinsert(X2,X3,X4),X2,X1,c_Set_Oinsert(X1,hAPP(X5,X3),c_Set_Oimage(X2,X1,X5,X4))),esk19_5(c_Set_Oinsert(X1,hAPP(X5,X3),c_Set_Oimage(X2,X1,X5,X4)),X6,X1,c_Set_Oimage(X1,X7,X6,c_Set_Oinsert(X1,hAPP(X5,X3),c_Set_Oimage(X2,X1,X5,X4))),X7)),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_1600,i_0_2567,i_0_1730,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174]) ).
cnf(i_0_2647,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,c_Set_Oimage(X1,X4,X3,X2),X4),X2),
inference(rename_variables,[],[i_0_2014]) ).
cnf(i_0_2648,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Fun_Oinj__on(X1,X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
inference(rename_variables,[],[i_0_1174]) ).
cnf(i_0_2649,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2090,i_0_2103,i_0_2471,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631]) ).
cnf(i_0_2650,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_1668]) ).
cnf(i_0_2651,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1631]) ).
cnf(i_0_2652,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478]) ).
cnf(i_0_2653,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X2),
inference(rename_variables,[],[i_0_2048]) ).
cnf(i_0_2654,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_1464]) ).
cnf(i_0_2655,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != hAPP(c_Nat_OSuc,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_1478]) ).
cnf(i_0_2656,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X4),X4),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246]) ).
cnf(i_0_2657,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X2),
inference(rename_variables,[],[i_0_2322]) ).
cnf(i_0_2658,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),
inference(rename_variables,[],[i_0_2037]) ).
cnf(i_0_2659,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4) ),
inference(rename_variables,[],[i_0_1246]) ).
cnf(i_0_2660,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),X1),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287]) ).
cnf(i_0_2661,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1287]) ).
cnf(i_0_2662,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X1),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2076,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485]) ).
cnf(i_0_2663,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1485]) ).
cnf(i_0_2664,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),X4),X1),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2076,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283]) ).
cnf(i_0_2665,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1283]) ).
cnf(i_0_2666,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2076,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436]) ).
cnf(i_0_2667,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(rename_variables,[],[i_0_2313]) ).
cnf(i_0_2668,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(rename_variables,[],[i_0_1436]) ).
cnf(i_0_2669,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),X2),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2076,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245]) ).
cnf(i_0_2670,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4) ),
inference(rename_variables,[],[i_0_1245]) ).
cnf(i_0_2671,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X1),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493]) ).
cnf(i_0_2672,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1493]) ).
cnf(i_0_2673,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Nat_OSuc,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618]) ).
cnf(i_0_2674,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1618]) ).
cnf(i_0_2675,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk23_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494]) ).
cnf(i_0_2676,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1494]) ).
cnf(i_0_2677,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489]) ).
cnf(i_0_2678,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1489]) ).
cnf(i_0_2679,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Nat_OSuc,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620]) ).
cnf(i_0_2680,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1620]) ).
cnf(i_0_2681,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)),X2),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401]) ).
cnf(i_0_2682,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X2),
inference(rename_variables,[],[i_0_2282]) ).
cnf(i_0_2683,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1401]) ).
cnf(i_0_2684,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558]) ).
cnf(i_0_2685,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2686,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),X3) != c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807]) ).
cnf(i_0_2687,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) != X1,
inference(rename_variables,[],[i_0_2008]) ).
cnf(i_0_2688,plain,
hAPP(c_Set_Oinsert(X1,X2,X3),X2) != c_fFalse,
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892]) ).
cnf(i_0_2689,plain,
class_Orderings_Oorder(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894]) ).
cnf(i_0_2690,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2691,plain,
class_Orderings_Olinorder(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895]) ).
cnf(i_0_2692,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2693,plain,
class_Rings_Ocomm__semiring__1(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896]) ).
cnf(i_0_2694,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2695,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897]) ).
cnf(i_0_2696,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2697,plain,
class_Groups_Oordered__ab__semigroup__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898]) ).
cnf(i_0_2698,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2699,plain,
class_Groups_Ocomm__monoid__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900]) ).
cnf(i_0_2700,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2701,plain,
class_Groups_Oordered__comm__monoid__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904]) ).
cnf(i_0_2702,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2703,plain,
class_Rings_Olinordered__semidom(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906]) ).
cnf(i_0_2704,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2705,plain,
class_Groups_Oab__semigroup__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908]) ).
cnf(i_0_2706,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2707,plain,
class_Orderings_Opreorder(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909]) ).
cnf(i_0_2708,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2709,plain,
class_Groups_Ocancel__semigroup__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910]) ).
cnf(i_0_2710,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2711,plain,
class_Groups_Ocancel__ab__semigroup__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911]) ).
cnf(i_0_2712,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2713,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912]) ).
cnf(i_0_2714,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2715,plain,
class_Orderings_Oord(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913]) ).
cnf(i_0_2716,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2717,plain,
class_Orderings_Obot(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914]) ).
cnf(i_0_2718,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2719,plain,
class_Finite__Set_Ofinite(c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916]) ).
cnf(i_0_2720,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2721,plain,
class_Groups_Omonoid__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917]) ).
cnf(i_0_2722,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2723,plain,
class_Rings_Ozero__neq__one(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918]) ).
cnf(i_0_2724,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2725,plain,
class_Groups_Oone(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919]) ).
cnf(i_0_2726,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2727,plain,
c_Arrow__Order__Mirabelle_Ounanimity(c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,v_F))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920]) ).
cnf(i_0_2728,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2729,plain,
c_Arrow__Order__Mirabelle_OIIA(c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,v_F))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921]) ).
cnf(i_0_2730,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2731,plain,
class_Groups_Ozero(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922]) ).
cnf(i_0_2732,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2733,plain,
~ c_member(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X2,c_Set_Oinsert(X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Nat_OSuc,X4)),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923]) ).
cnf(i_0_2734,plain,
~ c_member(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X2,X1,c_Nat_OSuc,X3)),
inference(rename_variables,[],[i_0_2208]) ).
cnf(i_0_2735,plain,
~ c_Orderings_Oord__class_Oless(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926]) ).
cnf(i_0_2736,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2737,plain,
~ c_Orderings_Oord__class_Oless__eq(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2349,i_0_2218,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929]) ).
cnf(i_0_2738,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2739,plain,
~ c_Orderings_Oord__class_Oless__eq(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930]) ).
cnf(i_0_2740,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2741,plain,
~ c_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935]) ).
cnf(i_0_2742,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2743,plain,
~ c_Finite__Set_Ofinite(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936]) ).
cnf(i_0_2744,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2745,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937]) ).
cnf(i_0_2746,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_2747,plain,
~ c_member(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk13_2(c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924]) ).
cnf(i_0_2748,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2749,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931]) ).
cnf(i_0_2750,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(rename_variables,[],[i_0_2313]) ).
cnf(i_0_2751,plain,
~ c_member(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X2,X1,c_Nat_OSuc,X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925]) ).
cnf(i_0_2752,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2753,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_Set_Oinsert(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927]) ).
cnf(i_0_2754,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),X2,X2),
inference(rename_variables,[],[i_0_2212]) ).
cnf(i_0_2755,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928]) ).
cnf(i_0_2756,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),X2,X2),
inference(rename_variables,[],[i_0_2212]) ).
cnf(i_0_2757,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X5,X3,c_Set_Oimage(X3,X6,X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X6))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095]) ).
cnf(i_0_2758,plain,
~ c_member(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rename_variables,[],[i_0_1520]) ).
cnf(i_0_2759,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,c_Set_Oimage(X1,X4,X3,X2),X4),X2),
inference(rename_variables,[],[i_0_2014]) ).
cnf(i_0_2760,plain,
( c_member(X1,hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5),X6)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X6)
| ~ c_member(X2,X5,c_Set_Oimage(X1,X2,X4,X3))
| ~ c_Fun_Oinj__on(X1,X2,X4,X3) ),
inference(rename_variables,[],[i_0_1095]) ).
cnf(i_0_2761,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),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_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422]) ).
cnf(i_0_2762,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(rename_variables,[],[i_0_1422]) ).
cnf(i_0_2763,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424]) ).
cnf(i_0_2764,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2150]) ).
cnf(i_0_2765,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1424]) ).
cnf(i_0_2766,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425]) ).
cnf(i_0_2767,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1425]) ).
cnf(i_0_2768,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2640,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426]) ).
cnf(i_0_2769,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(rename_variables,[],[i_0_2173]) ).
cnf(i_0_2770,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1426]) ).
cnf(i_0_2771,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),X2)),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2640,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428]) ).
cnf(i_0_2772,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),
inference(rename_variables,[],[i_0_2037]) ).
cnf(i_0_2773,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1428]) ).
cnf(i_0_2774,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2640,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551]) ).
cnf(i_0_2775,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(rename_variables,[],[i_0_2095]) ).
cnf(i_0_2776,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1551]) ).
cnf(i_0_2777,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2640,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613]) ).
cnf(i_0_2778,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Finite__Set_Ocard(X2,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_2043]) ).
cnf(i_0_2779,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1613]) ).
cnf(i_0_2780,plain,
c_Set_Oimage(X1,X2,esk8_4(c_Set_Oinsert(X1,X3,X4),X1,X2,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X1,X3,X4)) = c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4)),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2640,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099]) ).
cnf(i_0_2781,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1600]) ).
cnf(i_0_2782,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk9_4(c_Set_Oinsert(X1,X3,X4),X1,X2,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X1,X3,X4)),
inference(rename_variables,[],[i_0_2236]) ).
cnf(i_0_2783,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X3,X2,esk8_4(X4,X3,X2,X1),X4) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oimage(X2,X3,X5,X1),X4)
| ~ c_Fun_Oinj__on(X2,X3,X5,X1) ),
inference(rename_variables,[],[i_0_1099]) ).
cnf(i_0_2784,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2171,i_0_2173,i_0_2541,i_0_2640,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477]) ).
cnf(i_0_2785,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_1736]) ).
cnf(i_0_2786,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1477]) ).
cnf(i_0_2787,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3) != X1,
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2171,i_0_2173,i_0_2541,i_0_2640,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604]) ).
cnf(i_0_2788,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2164]) ).
cnf(i_0_2789,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1604]) ).
cnf(i_0_2790,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2171,i_0_2173,i_0_2541,i_0_2640,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276]) ).
cnf(i_0_2791,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3)),
inference(rename_variables,[],[i_0_2103]) ).
cnf(i_0_2792,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1276]) ).
cnf(i_0_2793,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2048,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450]) ).
cnf(i_0_2794,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(rename_variables,[],[i_0_2171]) ).
cnf(i_0_2795,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1450]) ).
cnf(i_0_2796,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X3),X1),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236]) ).
cnf(i_0_2797,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X1),
inference(rename_variables,[],[i_0_2045]) ).
cnf(i_0_2798,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1236]) ).
cnf(i_0_2799,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),X3),X2),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237]) ).
cnf(i_0_2800,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),X2),
inference(rename_variables,[],[i_0_2069]) ).
cnf(i_0_2801,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1237]) ).
cnf(i_0_2802,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274]) ).
cnf(i_0_2803,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1274]) ).
cnf(i_0_2804,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238]) ).
cnf(i_0_2805,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1238]) ).
cnf(i_0_2806,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)),X3),X4),X2),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299]) ).
cnf(i_0_2807,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2164]) ).
cnf(i_0_2808,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1299]) ).
cnf(i_0_2809,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368]) ).
cnf(i_0_2810,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2811,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2812,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_1542]) ).
cnf(i_0_2813,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(rename_variables,[],[i_0_1368]) ).
cnf(i_0_2814,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343]) ).
cnf(i_0_2815,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4) ),
inference(rename_variables,[],[i_0_1343]) ).
cnf(i_0_2816,plain,
~ c_member(X1,X2,esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X3,X1,c_Set_Oimage(X1,X4,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180]) ).
cnf(i_0_2817,plain,
( c_member(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))
| ~ c_member(X4,X3,X5) ),
inference(rename_variables,[],[i_0_1180]) ).
cnf(i_0_2818,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)) != hAPP(c_Nat_OSuc,c_Set_Oimage(X1,tc_Product__Type_Ounit,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687]) ).
cnf(i_0_2819,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(rename_variables,[],[i_0_1687]) ).
cnf(i_0_2820,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306]) ).
cnf(i_0_2821,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1306]) ).
cnf(i_0_2822,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460]) ).
cnf(i_0_2823,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(rename_variables,[],[i_0_1460]) ).
cnf(i_0_2824,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) != X1,
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827]) ).
cnf(i_0_2825,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X3,X4,X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),X2),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827,i_0_1304]) ).
cnf(i_0_2826,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1304]) ).
cnf(i_0_2827,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827,i_0_1304,i_0_1728]) ).
cnf(i_0_2828,plain,
( 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(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2829,plain,
( c_member(X1,X2,c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X4,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X4,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827,i_0_1304,i_0_1728,i_0_1247]) ).
cnf(i_0_2830,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X4,X3))
| c_member(X1,X4,X2) ),
inference(rename_variables,[],[i_0_1247]) ).
cnf(i_0_2831,plain,
c_member(tc_Product__Type_Ounit,esk42_2(hAPP(c_Nat_OSuc,c_Set_Oimage(X1,tc_Product__Type_Ounit,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),tc_Product__Type_Ounit),hAPP(c_Nat_OSuc,c_Set_Oimage(X1,tc_Product__Type_Ounit,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2633,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827,i_0_1304,i_0_1728,i_0_1247,i_0_1605]) ).
cnf(i_0_2832,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(rename_variables,[],[i_0_2136]) ).
cnf(i_0_2833,plain,
( c_Finite__Set_Ocard(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_member(X1,esk42_2(X2,X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1605]) ).
cnf(i_0_2834,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2612,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2633,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827,i_0_1304,i_0_1728,i_0_1247,i_0_1605,i_0_1445]) ).
cnf(i_0_2835,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))),
inference(rename_variables,[],[i_0_2034]) ).
cnf(i_0_2836,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1445]) ).
cnf(i_0_2837,plain,
( ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X4,X3,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X2) ),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2612,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2633,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827,i_0_1304,i_0_1728,i_0_1247,i_0_1605,i_0_1445,i_0_1326]) ).
cnf(i_0_2838,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X4,X3) ),
inference(rename_variables,[],[i_0_1326]) ).
cnf(i_0_2839,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_fun(X1,tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_fun(X1,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_fun(X1,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_fun(X1,tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_fun(X1,tc_Nat_Onat))) ),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2229,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2612,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2633,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827,i_0_1304,i_0_1728,i_0_1247,i_0_1605,i_0_1445,i_0_1326,i_0_1373]) ).
cnf(i_0_2840,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Nat_Onat),X2,X2),
inference(rename_variables,[],[i_0_2229]) ).
cnf(i_0_2841,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_1373]) ).
cnf(i_0_2842,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))),X2))) ),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2229,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2612,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2633,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827,i_0_1304,i_0_1728,i_0_1247,i_0_1605,i_0_1445,i_0_1326,i_0_1373,i_0_1374]) ).
cnf(i_0_2843,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))),X3)),
inference(rename_variables,[],[i_0_2245]) ).
cnf(i_0_2844,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_1374]) ).
cnf(i_0_2845,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_fun(X1,tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_fun(X1,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_fun(X1,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_fun(X1,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_fun(X1,tc_Nat_Onat)))) ),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2229,i_0_2840,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2612,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2633,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827,i_0_1304,i_0_1728,i_0_1247,i_0_1605,i_0_1445,i_0_1326,i_0_1373,i_0_1374,i_0_1375]) ).
cnf(i_0_2846,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Nat_Onat),X2,X2),
inference(rename_variables,[],[i_0_2229]) ).
cnf(i_0_2847,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_1375]) ).
cnf(i_0_2848,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(X1) ),
inference(scs_inference,[],[i_0_2141,i_0_2550,i_0_2144,i_0_2146,i_0_2003,i_0_2383,i_0_2385,i_0_2690,i_0_2692,i_0_2694,i_0_2696,i_0_2698,i_0_2700,i_0_2702,i_0_2704,i_0_2706,i_0_2708,i_0_2710,i_0_2712,i_0_2714,i_0_2716,i_0_2718,i_0_2720,i_0_2722,i_0_2724,i_0_2726,i_0_2728,i_0_2730,i_0_2732,i_0_2308,i_0_2159,i_0_2586,i_0_2150,i_0_2456,i_0_2764,i_0_2313,i_0_2481,i_0_2667,i_0_2228,i_0_2205,i_0_2204,i_0_2203,i_0_2202,i_0_2200,i_0_2199,i_0_2198,i_0_2197,i_0_2196,i_0_2195,i_0_2194,i_0_2193,i_0_2192,i_0_2191,i_0_2190,i_0_2189,i_0_2188,i_0_2208,i_0_2734,i_0_2316,i_0_2008,i_0_2444,i_0_2583,i_0_2212,i_0_2754,i_0_2187,i_0_2216,i_0_2563,i_0_2011,i_0_2224,i_0_2349,i_0_2218,i_0_2417,i_0_2365,i_0_2167,i_0_2164,i_0_2390,i_0_2434,i_0_2459,i_0_2486,i_0_2504,i_0_2516,i_0_2788,i_0_2171,i_0_2494,i_0_2173,i_0_2541,i_0_2640,i_0_2179,i_0_2210,i_0_2186,i_0_2220,i_0_2462,i_0_2222,i_0_2226,i_0_1961,i_0_1976,i_0_1795,i_0_1788,i_0_1731,i_0_2407,i_0_2414,i_0_2420,i_0_2428,i_0_2431,i_0_2437,i_0_2468,i_0_2476,i_0_2546,i_0_2600,i_0_2636,i_0_2736,i_0_2738,i_0_2740,i_0_2742,i_0_2744,i_0_2748,i_0_2752,i_0_2811,i_0_1755,i_0_1582,i_0_1711,i_0_1690,i_0_2017,i_0_2387,i_0_2242,i_0_2236,i_0_2229,i_0_2840,i_0_2014,i_0_2396,i_0_2564,i_0_2570,i_0_2609,i_0_2615,i_0_2647,i_0_2023,i_0_2100,i_0_2351,i_0_2272,i_0_2043,i_0_2037,i_0_2507,i_0_2510,i_0_2524,i_0_2658,i_0_2040,i_0_2501,i_0_2045,i_0_2048,i_0_2069,i_0_2090,i_0_2393,i_0_2103,i_0_2471,i_0_2603,i_0_2322,i_0_2245,i_0_2262,i_0_2425,i_0_2095,i_0_2034,i_0_2465,i_0_2612,i_0_2282,i_0_2532,i_0_2284,i_0_2293,i_0_2076,i_0_2057,i_0_2136,i_0_2549,i_0_2587,i_0_2619,i_0_2633,i_0_2327,i_0_1520,i_0_1542,i_0_2575,i_0_1405,i_0_1591,i_0_1668,i_0_2593,i_0_1736,i_0_1773,i_0_1600,i_0_2567,i_0_2580,i_0_1730,i_0_1464,i_0_1784,i_0_1780,i_0_1783,i_0_1779,i_0_1792,i_0_2375,i_0_2376,i_0_1171,i_0_1303,i_0_1305,i_0_1088,i_0_1114,i_0_1115,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1680,i_0_1714,i_0_1725,i_0_1760,i_0_1691,i_0_1332,i_0_1333,i_0_1410,i_0_1417,i_0_1641,i_0_1661,i_0_1665,i_0_1724,i_0_1170,i_0_1673,i_0_1674,i_0_1348,i_0_1412,i_0_1416,i_0_1443,i_0_1506,i_0_1507,i_0_1635,i_0_1664,i_0_1734,i_0_1414,i_0_1429,i_0_1535,i_0_1539,i_0_1574,i_0_1590,i_0_1660,i_0_1270,i_0_1447,i_0_1689,i_0_1351,i_0_1352,i_0_1510,i_0_1537,i_0_1581,i_0_1473,i_0_1511,i_0_1444,i_0_1448,i_0_1472,i_0_1512,i_0_1806,i_0_1825,i_0_1222,i_0_1282,i_0_1289,i_0_1644,i_0_1124,i_0_1226,i_0_1285,i_0_1288,i_0_1224,i_0_1284,i_0_1328,i_0_1129,i_0_1400,i_0_1573,i_0_1089,i_0_1101,i_0_1197,i_0_1693,i_0_1121,i_0_1496,i_0_1651,i_0_1653,i_0_1135,i_0_1220,i_0_1327,i_0_1382,i_0_1451,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1149,i_0_1702,i_0_1345,i_0_1486,i_0_1556,i_0_1174,i_0_1631,i_0_1478,i_0_1246,i_0_1287,i_0_1485,i_0_1283,i_0_1436,i_0_1245,i_0_1493,i_0_1618,i_0_1494,i_0_1489,i_0_1620,i_0_1401,i_0_1558,i_0_1807,i_0_1892,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1935,i_0_1936,i_0_1937,i_0_1924,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1426,i_0_1428,i_0_1551,i_0_1613,i_0_1099,i_0_1477,i_0_1604,i_0_1276,i_0_1450,i_0_1236,i_0_1237,i_0_1274,i_0_1238,i_0_1299,i_0_1368,i_0_1343,i_0_1180,i_0_1687,i_0_1306,i_0_1460,i_0_1827,i_0_1304,i_0_1728,i_0_1247,i_0_1605,i_0_1445,i_0_1326,i_0_1373,i_0_1374,i_0_1375,i_0_1695]) ).
cnf(i_0_2849,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2850,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(rename_variables,[],[i_0_1695]) ).
cnf(i_0_2851,plain,
hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X2,
inference(scs_inference,[],[i_0_2537,i_0_1828]) ).
cnf(i_0_2852,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) != X2,
inference(rename_variables,[],[i_0_2537]) ).
cnf(i_0_2853,plain,
hAPP(c_Nat_OSuc,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)) != X1,
inference(scs_inference,[],[i_0_2537,i_0_2478,i_0_1828,i_0_1878]) ).
cnf(i_0_2854,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)) != X1,
inference(rename_variables,[],[i_0_2478]) ).
cnf(i_0_2855,plain,
c_Fun_Oinj__on(X1,X2,X3,c_Set_Oimage(X4,X1,X5,c_Set_Oimage(X6,X4,X7,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2537,i_0_2478,i_0_2398,i_0_1828,i_0_1878,i_0_1171]) ).
cnf(i_0_2856,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Set_Oimage(X5,X3,X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_2398]) ).
cnf(i_0_2857,plain,
( c_member(X1,esk2_4(X2,X3,X4,X1),X2)
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(rename_variables,[],[i_0_1171]) ).
cnf(i_0_2858,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X2),
inference(scs_inference,[],[i_0_2537,i_0_2478,i_0_2652,i_0_2398,i_0_1828,i_0_1878,i_0_1171,i_0_1303]) ).
cnf(i_0_2859,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(rename_variables,[],[i_0_2652]) ).
cnf(i_0_2860,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1303]) ).
cnf(i_0_2861,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X1),
inference(scs_inference,[],[i_0_2537,i_0_2478,i_0_2652,i_0_2398,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305]) ).
cnf(i_0_2862,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X3),X1),
inference(rename_variables,[],[i_0_2796]) ).
cnf(i_0_2863,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1305]) ).
cnf(i_0_2864,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2537,i_0_2478,i_0_2652,i_0_2398,i_0_2814,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687]) ).
cnf(i_0_2865,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(rename_variables,[],[i_0_1687]) ).
cnf(i_0_2866,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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(scs_inference,[],[i_0_2537,i_0_2478,i_0_2652,i_0_2398,i_0_2814,i_0_2638,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728]) ).
cnf(i_0_2867,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2638]) ).
cnf(i_0_2868,plain,
( 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(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2869,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3),X2),
inference(scs_inference,[],[i_0_2537,i_0_2478,i_0_2652,i_0_2398,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304]) ).
cnf(i_0_2870,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)),X2),
inference(rename_variables,[],[i_0_2681]) ).
cnf(i_0_2871,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1304]) ).
cnf(i_0_2872,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(c_Set_Oinsert(X1,X2,X3),X4,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Set_Oimage(X1,X5,X4,X3)),X5),c_Set_Oinsert(X1,X2,X3)),
inference(scs_inference,[],[i_0_2537,i_0_2478,i_0_2652,i_0_2398,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088]) ).
cnf(i_0_2873,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X3,X1,X4,X5))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),esk19_5(X5,X4,X3,X2,X1),X5) ),
inference(rename_variables,[],[i_0_1088]) ).
cnf(i_0_2874,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Set_Oimage(X5,X3,X6,c_Set_Oimage(X7,X5,X8,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),
inference(scs_inference,[],[i_0_2537,i_0_2478,i_0_2652,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114]) ).
cnf(i_0_2875,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Set_Oimage(X5,X3,X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_2398]) ).
cnf(i_0_2876,plain,
( c_member(X1,esk18_4(X2,X3,X1,X4),X2)
| ~ c_member(X5,X4,c_Set_Oimage(X1,X5,X3,X2)) ),
inference(rename_variables,[],[i_0_1114]) ).
cnf(i_0_2877,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2537,i_0_2478,i_0_2652,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125]) ).
cnf(i_0_2878,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2),c_Set_Oimage(X1,X4,X5,X3)) ),
inference(rename_variables,[],[i_0_1125]) ).
cnf(i_0_2879,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2537,i_0_2478,i_0_2652,i_0_2031,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588]) ).
cnf(i_0_2880,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_member(X2,X3,X1) ),
inference(rename_variables,[],[i_0_1588]) ).
cnf(i_0_2881,plain,
c_member(X1,esk17_2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2537,i_0_2852,i_0_2478,i_0_2652,i_0_2031,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632]) ).
cnf(i_0_2882,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) != X2,
inference(rename_variables,[],[i_0_2537]) ).
cnf(i_0_2883,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_member(X2,esk17_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_1632]) ).
cnf(i_0_2884,plain,
c_member(X1,esk16_2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2537,i_0_2852,i_0_2882,i_0_2478,i_0_2652,i_0_2031,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633]) ).
cnf(i_0_2885,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) != X2,
inference(rename_variables,[],[i_0_2537]) ).
cnf(i_0_2886,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_member(X2,esk16_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_1633]) ).
cnf(i_0_2887,plain,
c_Finite__Set_Ocard(X1,esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,X1,c_Set_Oimage(X1,X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2569,i_0_2537,i_0_2852,i_0_2882,i_0_2478,i_0_2652,i_0_2031,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725]) ).
cnf(i_0_2888,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1725]) ).
cnf(i_0_2889,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X4),X2),
inference(scs_inference,[],[i_0_2569,i_0_2537,i_0_2852,i_0_2882,i_0_2478,i_0_2652,i_0_2859,i_0_2031,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410]) ).
cnf(i_0_2890,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(rename_variables,[],[i_0_2652]) ).
cnf(i_0_2891,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1410]) ).
cnf(i_0_2892,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Set_Othe__elem(X2,c_Set_Oinsert(X2,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2569,i_0_2537,i_0_2852,i_0_2882,i_0_2478,i_0_2652,i_0_2859,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417]) ).
cnf(i_0_2893,plain,
c_Set_Othe__elem(X1,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2,
inference(rename_variables,[],[i_0_1430]) ).
cnf(i_0_2894,plain,
( X1 != hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1417]) ).
cnf(i_0_2895,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),X3)) != X1,
inference(scs_inference,[],[i_0_2569,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2478,i_0_2652,i_0_2859,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665]) ).
cnf(i_0_2896,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3) != X1,
inference(rename_variables,[],[i_0_2787]) ).
cnf(i_0_2897,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
inference(rename_variables,[],[i_0_1665]) ).
cnf(i_0_2898,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_2569,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2478,i_0_2652,i_0_2859,i_0_2340,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680]) ).
cnf(i_0_2899,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(rename_variables,[],[i_0_1680]) ).
cnf(i_0_2900,plain,
~ class_Orderings_Otop(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2569,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2478,i_0_2737,i_0_2652,i_0_2859,i_0_2340,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714]) ).
cnf(i_0_2901,plain,
~ c_Orderings_Oord__class_Oless__eq(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(rename_variables,[],[i_0_2737]) ).
cnf(i_0_2902,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Orderings_Otop__class_Otop(X1))
| ~ class_Orderings_Otop(X1) ),
inference(rename_variables,[],[i_0_1714]) ).
cnf(i_0_2903,plain,
c_Orderings_Oord__class_Oless__eq(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),X1,X1),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2478,i_0_2737,i_0_2652,i_0_2859,i_0_2340,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724]) ).
cnf(i_0_2904,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(rename_variables,[],[i_0_1724]) ).
cnf(i_0_2905,plain,
c_Finite__Set_Ofinite(c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X1),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2340,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760]) ).
cnf(i_0_2906,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2907,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2340,i_0_2079,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673]) ).
cnf(i_0_2908,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_1673]) ).
cnf(i_0_2909,plain,
~ c_member(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X2,X1,c_Nat_OSuc,X3)),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2340,i_0_2079,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115]) ).
cnf(i_0_2910,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_2424]) ).
cnf(i_0_2911,plain,
( X1 = hAPP(X2,esk18_4(X3,X2,X4,X1))
| ~ c_member(X5,X1,c_Set_Oimage(X4,X5,X2,X3)) ),
inference(rename_variables,[],[i_0_1115]) ).
cnf(i_0_2912,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X3,esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X4,X2,c_Set_Oimage(X2,X5,X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X5)),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2340,i_0_2079,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332]) ).
cnf(i_0_2913,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = c_Set_Oimage(X2,X3,X4,X1) ),
inference(rename_variables,[],[i_0_1332]) ).
cnf(i_0_2914,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2340,i_0_2079,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348]) ).
cnf(i_0_2915,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_2079]) ).
cnf(i_0_2916,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1348]) ).
cnf(i_0_2917,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X4),X3),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2340,i_0_2079,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412]) ).
cnf(i_0_2918,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(rename_variables,[],[i_0_2652]) ).
cnf(i_0_2919,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1412]) ).
cnf(i_0_2920,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,X1,c_Set_Oimage(X1,X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2340,i_0_2079,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506]) ).
cnf(i_0_2921,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1)) ),
inference(rename_variables,[],[i_0_1506]) ).
cnf(i_0_2922,plain,
c_Fun_Oinj__on(X1,X2,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2340,i_0_2079,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170]) ).
cnf(i_0_2923,plain,
~ c_member(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_2406]) ).
cnf(i_0_2924,plain,
( c_member(X1,esk3_4(X2,X3,X4,X1),X2)
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(rename_variables,[],[i_0_1170]) ).
cnf(i_0_2925,plain,
c_Set_Oimage(X1,X2,X3,esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4,X1,c_Set_Oimage(X1,X5,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X5)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2340,i_0_2079,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333]) ).
cnf(i_0_2926,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X2,X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_1333]) ).
cnf(i_0_2927,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X1),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2220,i_0_2340,i_0_2079,i_0_2031,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414]) ).
cnf(i_0_2928,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1),
inference(rename_variables,[],[i_0_2220]) ).
cnf(i_0_2929,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1414]) ).
cnf(i_0_2930,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),hAPP(c_Nat_OSuc,X4))),X3),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2220,i_0_2340,i_0_2079,i_0_2031,i_0_2320,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416]) ).
cnf(i_0_2931,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X3))),X2),
inference(rename_variables,[],[i_0_2320]) ).
cnf(i_0_2932,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1416]) ).
cnf(i_0_2933,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507]) ).
cnf(i_0_2934,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_2079]) ).
cnf(i_0_2935,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1507]) ).
cnf(i_0_2936,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X3),X2),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535]) ).
cnf(i_0_2937,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(rename_variables,[],[i_0_2652]) ).
cnf(i_0_2938,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1535]) ).
cnf(i_0_2939,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2749,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635]) ).
cnf(i_0_2940,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1635]) ).
cnf(i_0_2941,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2749,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674]) ).
cnf(i_0_2942,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(rename_variables,[],[i_0_1674]) ).
cnf(i_0_2943,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2749,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734]) ).
cnf(i_0_2944,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_1734]) ).
cnf(i_0_2945,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2749,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429]) ).
cnf(i_0_2946,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3) != X1,
inference(rename_variables,[],[i_0_2787]) ).
cnf(i_0_2947,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
inference(rename_variables,[],[i_0_1429]) ).
cnf(i_0_2948,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)),X1),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2749,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539]) ).
cnf(i_0_2949,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1),
inference(rename_variables,[],[i_0_2051]) ).
cnf(i_0_2950,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1539]) ).
cnf(i_0_2951,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X3)),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2749,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590]) ).
cnf(i_0_2952,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(rename_variables,[],[i_0_2652]) ).
cnf(i_0_2953,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1590]) ).
cnf(i_0_2954,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,esk19_5(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,X2,X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2749,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661]) ).
cnf(i_0_2955,plain,
~ c_member(X1,X2,esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X3,X1,c_Set_Oimage(X1,X4,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)),
inference(rename_variables,[],[i_0_2816]) ).
cnf(i_0_2956,plain,
( c_member(tc_Nat_Onat,esk13_2(X1,X2),X1)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(rename_variables,[],[i_0_1661]) ).
cnf(i_0_2957,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2749,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664]) ).
cnf(i_0_2958,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1664]) ).
cnf(i_0_2959,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X3) != X2,
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2749,i_0_2220,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689]) ).
cnf(i_0_2960,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(rename_variables,[],[i_0_2652]) ).
cnf(i_0_2961,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1689]) ).
cnf(i_0_2962,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X4))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2749,i_0_2220,i_0_2085,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352]) ).
cnf(i_0_2963,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))),
inference(rename_variables,[],[i_0_2085]) ).
cnf(i_0_2964,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1352]) ).
cnf(i_0_2965,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X2),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2749,i_0_2220,i_0_2085,i_0_2353,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447]) ).
cnf(i_0_2966,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_2353]) ).
cnf(i_0_2967,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1447]) ).
cnf(i_0_2968,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X3),X2),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2353,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537]) ).
cnf(i_0_2969,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(rename_variables,[],[i_0_2652]) ).
cnf(i_0_2970,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1537]) ).
cnf(i_0_2971,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,hAPP(c_Nat_OSuc,c_Set_Oimage(X3,X1,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2353,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270]) ).
cnf(i_0_2972,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2),X3) ),
inference(rename_variables,[],[i_0_1270]) ).
cnf(i_0_2973,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X1,tc_Nat_Onat,X2,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2353,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660]) ).
cnf(i_0_2974,plain,
( c_member(tc_Nat_Onat,esk15_2(X1,X2),X1)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(rename_variables,[],[i_0_1660]) ).
cnf(i_0_2975,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2)),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2353,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510]) ).
cnf(i_0_2976,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)),
inference(rename_variables,[],[i_0_2300]) ).
cnf(i_0_2977,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1510]) ).
cnf(i_0_2978,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Set_Othe__elem(X2,c_Set_Oinsert(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2353,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574]) ).
cnf(i_0_2979,plain,
c_Set_Othe__elem(X1,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2,
inference(rename_variables,[],[i_0_1430]) ).
cnf(i_0_2980,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1574]) ).
cnf(i_0_2981,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2353,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581]) ).
cnf(i_0_2982,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1581]) ).
cnf(i_0_2983,plain,
esk23_2(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(c_Nat_OSuc,X1),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2353,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691]) ).
cnf(i_0_2984,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(rename_variables,[],[i_0_1691]) ).
cnf(i_0_2985,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X4))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351]) ).
cnf(i_0_2986,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))),
inference(rename_variables,[],[i_0_2085]) ).
cnf(i_0_2987,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1351]) ).
cnf(i_0_2988,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X1),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473]) ).
cnf(i_0_2989,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1473]) ).
cnf(i_0_2990,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511]) ).
cnf(i_0_2991,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_2353]) ).
cnf(i_0_2992,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1511]) ).
cnf(i_0_2993,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(scs_inference,[],[i_0_2569,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512]) ).
cnf(i_0_2994,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1512]) ).
cnf(i_0_2995,plain,
c_Arrow__Order__Mirabelle_Ounanimity(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_F,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2569,i_0_2573,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375]) ).
cnf(i_0_2996,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_2997,plain,
c_Arrow__Order__Mirabelle_OIIA(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_F,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376]) ).
cnf(i_0_2998,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_2999,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X3) != X1,
inference(scs_inference,[],[i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827]) ).
cnf(i_0_3000,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X3) != X1,
inference(rename_variables,[],[i_0_2503]) ).
cnf(i_0_3001,plain,
c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5)) = c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5)),
inference(scs_inference,[],[i_0_2780,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806]) ).
cnf(i_0_3002,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,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(scs_inference,[],[i_0_2780,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645]) ).
cnf(i_0_3003,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X3) != X1,
inference(rename_variables,[],[i_0_2503]) ).
cnf(i_0_3004,plain,
( 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(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3005,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2780,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715]) ).
cnf(i_0_3006,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X3) != X1,
inference(rename_variables,[],[i_0_2503]) ).
cnf(i_0_3007,plain,
( 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(rename_variables,[],[i_0_1715]) ).
cnf(i_0_3008,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),hAPP(c_Nat_OSuc,X4)),X3),
inference(scs_inference,[],[i_0_2780,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290]) ).
cnf(i_0_3009,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_1290]) ).
cnf(i_0_3010,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),X2),
inference(scs_inference,[],[i_0_2780,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2669,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286]) ).
cnf(i_0_3011,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),X2),
inference(rename_variables,[],[i_0_2669]) ).
cnf(i_0_3012,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_1286]) ).
cnf(i_0_3013,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3))),
inference(scs_inference,[],[i_0_2780,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2669,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222]) ).
cnf(i_0_3014,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1222]) ).
cnf(i_0_3015,plain,
c_Finite__Set_Ofinite(X1,esk19_5(c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4)),X5,X1,c_Set_Oimage(X1,X6,X5,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4))),X6)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2669,i_0_2136,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124]) ).
cnf(i_0_3016,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(rename_variables,[],[i_0_2136]) ).
cnf(i_0_3017,plain,
c_Fun_Oinj__on(X1,X2,esk9_4(c_Set_Oinsert(X2,X3,X4),X2,X1,c_Set_Oinsert(X1,hAPP(X5,X3),c_Set_Oimage(X2,X1,X5,X4))),esk19_5(c_Set_Oinsert(X1,hAPP(X5,X3),c_Set_Oimage(X2,X1,X5,X4)),X6,X1,c_Set_Oimage(X1,X7,X6,c_Set_Oinsert(X1,hAPP(X5,X3),c_Set_Oimage(X2,X1,X5,X4))),X7)),
inference(rename_variables,[],[i_0_2646]) ).
cnf(i_0_3018,plain,
( ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,X4))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4)
| c_Finite__Set_Ofinite(X2,X4) ),
inference(rename_variables,[],[i_0_1124]) ).
cnf(i_0_3019,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2669,i_0_2136,i_0_1780,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289]) ).
cnf(i_0_3020,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1289]) ).
cnf(i_0_3021,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2669,i_0_2136,i_0_1780,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644]) ).
cnf(i_0_3022,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_3023,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = 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))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1644]) ).
cnf(i_0_3024,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2669,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285]) ).
cnf(i_0_3025,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1285]) ).
cnf(i_0_3026,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2669,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288]) ).
cnf(i_0_3027,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),X3),X2),
inference(rename_variables,[],[i_0_2799]) ).
cnf(i_0_3028,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_1288]) ).
cnf(i_0_3029,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)),X4)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2669,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226]) ).
cnf(i_0_3030,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1226]) ).
cnf(i_0_3031,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X4),X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2458,i_0_2669,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284]) ).
cnf(i_0_3032,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3),X4),X2),
inference(rename_variables,[],[i_0_2458]) ).
cnf(i_0_3033,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_1284]) ).
cnf(i_0_3034,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224]) ).
cnf(i_0_3035,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3)),
inference(rename_variables,[],[i_0_2523]) ).
cnf(i_0_3036,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1224]) ).
cnf(i_0_3037,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2347,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515]) ).
cnf(i_0_3038,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1515]) ).
cnf(i_0_3039,plain,
c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Set_Oimage(X1,X2,X3,c_Set_Oinsert(X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2347,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400]) ).
cnf(i_0_3040,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X3,c_Set_Oinsert(X2,X5,X4))),
inference(rename_variables,[],[i_0_2023]) ).
cnf(i_0_3041,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2)
| X2 = X3 ),
inference(rename_variables,[],[i_0_1400]) ).
cnf(i_0_3042,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5)),c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2347,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651]) ).
cnf(i_0_3043,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1651]) ).
cnf(i_0_3044,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Set_Oimage(X1,X2,esk8_4(c_Set_Oinsert(X1,X3,X4),X1,X2,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X1,X3,X4)),c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2347,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653]) ).
cnf(i_0_3045,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1653]) ).
cnf(i_0_3046,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X2,X1,X3,X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X2,X1,X3,X4)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2347,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2478,i_0_2737,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135]) ).
cnf(i_0_3047,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_3048,plain,
( X1 != c_Set_Oimage(X2,X3,X4,X5)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oimage(X2,X3,X4,X6))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X5,X6) ),
inference(rename_variables,[],[i_0_1135]) ).
cnf(i_0_3049,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2347,i_0_2707,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197]) ).
cnf(i_0_3050,plain,
hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X1,
inference(rename_variables,[],[i_0_2006]) ).
cnf(i_0_3051,plain,
( X1 = c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_3052,plain,
c_member(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(X2,X3)),c_Set_Oinsert(X1,X4,c_Set_Oimage(X5,X1,X2,c_fequal(X3)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2347,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1592,i_0_1469,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382]) ).
cnf(i_0_3053,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_3054,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X4,X2)
| c_member(X1,X4,X3) ),
inference(rename_variables,[],[i_0_1382]) ).
cnf(i_0_3055,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2347,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451]) ).
cnf(i_0_3056,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) != X2,
inference(rename_variables,[],[i_0_2537]) ).
cnf(i_0_3057,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(rename_variables,[],[i_0_1694]) ).
cnf(i_0_3058,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(X2,X1),X2) ),
inference(rename_variables,[],[i_0_1451]) ).
cnf(i_0_3059,plain,
c_Finite__Set_Ocard(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Set_Oimage(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2159,i_0_2347,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2422,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693]) ).
cnf(i_0_3060,plain,
hAPP(c_Nat_OSuc,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(rename_variables,[],[i_0_2159]) ).
cnf(i_0_3061,plain,
c_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(rename_variables,[],[i_0_2422]) ).
cnf(i_0_3062,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_1693]) ).
cnf(i_0_3063,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_2347,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2422,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496]) ).
cnf(i_0_3064,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))),
inference(rename_variables,[],[i_0_2034]) ).
cnf(i_0_3065,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),X3) != c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_2686]) ).
cnf(i_0_3066,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = X1 ),
inference(rename_variables,[],[i_0_1496]) ).
cnf(i_0_3067,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))),X2,X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_2347,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2406,i_0_2239,i_0_2422,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089]) ).
cnf(i_0_3068,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk6_4(X3,X2,X4,X1)),hAPP(X3,esk6_4(X3,X2,X4,X1)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ class_Orderings_Oord(X1) ),
inference(rename_variables,[],[i_0_1089]) ).
cnf(i_0_3069,plain,
c_Finite__Set_Ofinite(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Set_Oimage(X2,X1,X3,c_Set_Oimage(tc_Product__Type_Ounit,X2,X4,X5)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_2347,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149]) ).
cnf(i_0_3070,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Set_Oimage(X2,X1,X3,X4)),c_Set_Oimage(X2,X1,X3,c_Set_Oinsert(X2,X5,X4))),
inference(rename_variables,[],[i_0_2239]) ).
cnf(i_0_3071,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X3,X1,X4,X5))
| c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X5) ),
inference(rename_variables,[],[i_0_1149]) ).
cnf(i_0_3072,plain,
~ c_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oinsert(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_2347,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541]) ).
cnf(i_0_3073,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_3074,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(rename_variables,[],[i_0_1541]) ).
cnf(i_0_3075,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Set_Oimage(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_3060,i_0_2347,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583]) ).
cnf(i_0_3076,plain,
hAPP(c_Nat_OSuc,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(rename_variables,[],[i_0_2159]) ).
cnf(i_0_3077,plain,
c_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(rename_variables,[],[i_0_2422]) ).
cnf(i_0_3078,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_1583]) ).
cnf(i_0_3079,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_3060,i_0_2347,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654]) ).
cnf(i_0_3080,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1654]) ).
cnf(i_0_3081,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_3060,i_0_2347,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655]) ).
cnf(i_0_3082,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1655]) ).
cnf(i_0_3083,plain,
c_Orderings_Oord__class_Oless__eq(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5)),c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_3060,i_0_2347,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719]) ).
cnf(i_0_3084,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1719]) ).
cnf(i_0_3085,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Set_Oimage(X1,X2,esk8_4(c_Set_Oinsert(X1,X3,X4),X1,X2,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X1,X3,X4)),c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_3060,i_0_2347,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720]) ).
cnf(i_0_3086,plain,
( ~ class_Orderings_Opreorder(X1)
| X2 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1720]) ).
cnf(i_0_3087,plain,
c_Orderings_Oord__class_Oless__eq(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Set_Oimage(X1,X2,esk8_4(c_Set_Oinsert(X1,X3,X4),X1,X2,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X1,X3,X4)),c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_3060,i_0_2347,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2638,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721]) ).
cnf(i_0_3088,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1721]) ).
cnf(i_0_3089,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2159,i_0_3060,i_0_2347,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220]) ).
cnf(i_0_3090,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2455]) ).
cnf(i_0_3091,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1220]) ).
cnf(i_0_3092,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,esk9_4(c_Set_Oinsert(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Set_Oinsert(tc_Nat_Onat,X2,X3))),tc_Nat_Onat,tc_Nat_Onat,c_Set_Oinsert(tc_Nat_Onat,X2,X3)),X3),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2159,i_0_3060,i_0_2347,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174]) ).
cnf(i_0_3093,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_3094,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Fun_Oinj__on(X1,X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
inference(rename_variables,[],[i_0_1174]) ).
cnf(i_0_3095,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2159,i_0_3060,i_0_2347,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702]) ).
cnf(i_0_3096,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(rename_variables,[],[i_0_1702]) ).
cnf(i_0_3097,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436]) ).
cnf(i_0_3098,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(rename_variables,[],[i_0_2179]) ).
cnf(i_0_3099,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(rename_variables,[],[i_0_1436]) ).
cnf(i_0_3100,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3)),esk23_2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3)),hAPP(c_Nat_OSuc,X2))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1731,i_0_3022,i_0_2031,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486]) ).
cnf(i_0_3101,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1486]) ).
cnf(i_0_3102,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478]) ).
cnf(i_0_3103,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1677]) ).
cnf(i_0_3104,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != hAPP(c_Nat_OSuc,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_1478]) ).
cnf(i_0_3105,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X3),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345]) ).
cnf(i_0_3106,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(rename_variables,[],[i_0_1335]) ).
cnf(i_0_3107,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(rename_variables,[],[i_0_2652]) ).
cnf(i_0_3108,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_1345]) ).
cnf(i_0_3109,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2523,i_0_2458,i_0_2669,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618]) ).
cnf(i_0_3110,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1618]) ).
cnf(i_0_3111,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3),X4),X5)),X6),X6),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2523,i_0_2458,i_0_2669,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246]) ).
cnf(i_0_3112,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X4),X4),
inference(rename_variables,[],[i_0_2656]) ).
cnf(i_0_3113,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))),
inference(rename_variables,[],[i_0_2085]) ).
cnf(i_0_3114,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4) ),
inference(rename_variables,[],[i_0_1246]) ).
cnf(i_0_3115,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2523,i_0_2458,i_0_2669,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287]) ).
cnf(i_0_3116,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(rename_variables,[],[i_0_2500]) ).
cnf(i_0_3117,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1287]) ).
cnf(i_0_3118,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2523,i_0_2458,i_0_2669,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494]) ).
cnf(i_0_3119,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1494]) ).
cnf(i_0_3120,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk23_2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3)),hAPP(c_Nat_OSuc,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2523,i_0_2458,i_0_2669,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556]) ).
cnf(i_0_3121,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1556]) ).
cnf(i_0_3122,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2523,i_0_2458,i_0_2669,i_0_2493,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485]) ).
cnf(i_0_3123,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1485]) ).
cnf(i_0_3124,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(X1,esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,X1,c_Set_Oimage(X1,X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2523,i_0_2458,i_0_2669,i_0_2493,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573]) ).
cnf(i_0_3125,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_1736]) ).
cnf(i_0_3126,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1573]) ).
cnf(i_0_3127,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X3),X1),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283]) ).
cnf(i_0_3128,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X3),X1),
inference(rename_variables,[],[i_0_2485]) ).
cnf(i_0_3129,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1283]) ).
cnf(i_0_3130,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620]) ).
cnf(i_0_3131,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1620]) ).
cnf(i_0_3132,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,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(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493]) ).
cnf(i_0_3133,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1493]) ).
cnf(i_0_3134,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk23_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401]) ).
cnf(i_0_3135,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2150]) ).
cnf(i_0_3136,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1401]) ).
cnf(i_0_3137,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245]) ).
cnf(i_0_3138,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4) ),
inference(rename_variables,[],[i_0_1245]) ).
cnf(i_0_3139,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)),X3)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558]) ).
cnf(i_0_3140,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_3141,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1,X1),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489]) ).
cnf(i_0_3142,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1489]) ).
cnf(i_0_3143,plain,
tc_HOL_Obool != c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915]) ).
cnf(i_0_3144,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),X6),X7) != c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807]) ).
cnf(i_0_3145,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3) != X1,
inference(rename_variables,[],[i_0_2787]) ).
cnf(i_0_3146,plain,
class_Orderings_Oorder(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894]) ).
cnf(i_0_3147,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3148,plain,
class_Orderings_Olinorder(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895]) ).
cnf(i_0_3149,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3150,plain,
class_Rings_Ocomm__semiring__1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896]) ).
cnf(i_0_3151,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3152,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897]) ).
cnf(i_0_3153,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3154,plain,
class_Groups_Oordered__ab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898]) ).
cnf(i_0_3155,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3156,plain,
class_Groups_Ocomm__monoid__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900]) ).
cnf(i_0_3157,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3158,plain,
class_Groups_Oordered__comm__monoid__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904]) ).
cnf(i_0_3159,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3160,plain,
class_Rings_Olinordered__semidom(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906]) ).
cnf(i_0_3161,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3162,plain,
class_Groups_Oab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908]) ).
cnf(i_0_3163,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3164,plain,
class_Orderings_Opreorder(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909]) ).
cnf(i_0_3165,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3166,plain,
class_Groups_Ocancel__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910]) ).
cnf(i_0_3167,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3168,plain,
class_Groups_Ocancel__ab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911]) ).
cnf(i_0_3169,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3170,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912]) ).
cnf(i_0_3171,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3172,plain,
class_Orderings_Oord(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913]) ).
cnf(i_0_3173,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3174,plain,
class_Orderings_Obot(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914]) ).
cnf(i_0_3175,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3176,plain,
class_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,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(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916]) ).
cnf(i_0_3177,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3178,plain,
class_Groups_Omonoid__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917]) ).
cnf(i_0_3179,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3180,plain,
class_Rings_Ozero__neq__one(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918]) ).
cnf(i_0_3181,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3182,plain,
class_Groups_Oone(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919]) ).
cnf(i_0_3183,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3184,plain,
class_Groups_Ozero(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922]) ).
cnf(i_0_3185,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3186,plain,
~ c_member(c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X3,c_Set_Oinsert(X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Nat_OSuc,X5)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2195,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923]) ).
cnf(i_0_3187,plain,
~ c_member(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X2,c_Set_Oinsert(X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Nat_OSuc,X4)),
inference(rename_variables,[],[i_0_2733]) ).
cnf(i_0_3188,plain,
~ c_Orderings_Oord__class_Oless__eq(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,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(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_2686,i_0_2566,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2222,i_0_2195,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929]) ).
cnf(i_0_3189,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_3190,plain,
~ c_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_2686,i_0_2566,i_0_2003,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2222,i_0_2195,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936]) ).
cnf(i_0_3191,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_3192,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_2686,i_0_2566,i_0_2003,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937]) ).
cnf(i_0_3193,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3194,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) != c_fFalse,
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_2686,i_0_2566,i_0_2003,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892]) ).
cnf(i_0_3195,plain,
c_Arrow__Order__Mirabelle_Ounanimity(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,v_F)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_2686,i_0_2566,i_0_2003,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920]) ).
cnf(i_0_3196,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3197,plain,
c_Arrow__Order__Mirabelle_OIIA(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,v_F)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921]) ).
cnf(i_0_3198,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3199,plain,
~ c_Orderings_Oord__class_Oless(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),c_Set_Oimage(X3,X2,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926]) ).
cnf(i_0_3200,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_3201,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930]) ).
cnf(i_0_3202,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_3203,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935]) ).
cnf(i_0_3204,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_3205,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931]) ).
cnf(i_0_3206,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(rename_variables,[],[i_0_2313]) ).
cnf(i_0_3207,plain,
~ c_member(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X2,c_Set_Oinsert(X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Nat_OSuc,X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925]) ).
cnf(i_0_3208,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_3209,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),esk19_5(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X3,X2,c_Set_Oimage(X2,X4,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X4),c_Set_Oimage(X5,X2,X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927]) ).
cnf(i_0_3210,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),c_Set_Oimage(X3,X2,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_2214]) ).
cnf(i_0_3211,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X3,X2,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928]) ).
cnf(i_0_3212,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_3213,plain,
~ c_member(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Set_Oimage(X2,c_Set_Oinsert(X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Nat_OSuc,X4)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2693,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924]) ).
cnf(i_0_3214,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(rename_variables,[],[i_0_2003]) ).
cnf(i_0_3215,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Set_Oinsert(X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_2693,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423]) ).
cnf(i_0_3216,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Set_Oinsert(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(rename_variables,[],[i_0_2625]) ).
cnf(i_0_3217,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(rename_variables,[],[i_0_1423]) ).
cnf(i_0_3218,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3))),X3),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_2693,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235]) ).
cnf(i_0_3219,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1235]) ).
cnf(i_0_3220,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),X1)),X1),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_2693,i_0_2623,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298]) ).
cnf(i_0_3221,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1,X1),
inference(rename_variables,[],[i_0_2446]) ).
cnf(i_0_3222,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(rename_variables,[],[i_0_2623]) ).
cnf(i_0_3223,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1298]) ).
cnf(i_0_3224,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_2693,i_0_2623,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300]) ).
cnf(i_0_3225,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1,X1),
inference(rename_variables,[],[i_0_2446]) ).
cnf(i_0_3226,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1300]) ).
cnf(i_0_3227,plain,
~ c_member(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_2693,i_0_2623,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1405,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095]) ).
cnf(i_0_3228,plain,
~ c_member(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_2406]) ).
cnf(i_0_3229,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1692]) ).
cnf(i_0_3230,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1405]) ).
cnf(i_0_3231,plain,
( c_member(X1,hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5),X6)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X6)
| ~ c_member(X2,X5,c_Set_Oimage(X1,X2,X4,X3))
| ~ c_Fun_Oinj__on(X1,X2,X4,X3) ),
inference(rename_variables,[],[i_0_1095]) ).
cnf(i_0_3232,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Set_Oimage(X1,X2,esk8_4(c_Set_Oinsert(X1,X3,X4),X1,X2,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X1,X3,X4)),c_Set_Oimage(X1,X2,esk8_4(c_Set_Oinsert(X1,X3,X4),X1,X2,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X1,X3,X4))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_2693,i_0_2623,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1405,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422]) ).
cnf(i_0_3233,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(rename_variables,[],[i_0_1422]) ).
cnf(i_0_3234,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_2693,i_0_2623,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1405,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424]) ).
cnf(i_0_3235,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2150]) ).
cnf(i_0_3236,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1424]) ).
cnf(i_0_3237,plain,
~ c_Orderings_Oord__class_Oless(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5)),c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_2693,i_0_2623,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1405,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425]) ).
cnf(i_0_3238,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1425]) ).
cnf(i_0_3239,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Set_Oinsert(X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1405,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428]) ).
cnf(i_0_3240,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Set_Oinsert(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(rename_variables,[],[i_0_2625]) ).
cnf(i_0_3241,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1428]) ).
cnf(i_0_3242,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356]) ).
cnf(i_0_3243,plain,
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(rename_variables,[],[i_0_1591]) ).
cnf(i_0_3244,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X4,X3)
| ~ class_Orderings_Oord(X2) ),
inference(rename_variables,[],[i_0_1356]) ).
cnf(i_0_3245,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613]) ).
cnf(i_0_3246,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2638]) ).
cnf(i_0_3247,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(rename_variables,[],[i_0_1398]) ).
cnf(i_0_3248,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 = X2
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1613]) ).
cnf(i_0_3249,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,esk8_4(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))),tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),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)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_3229,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099]) ).
cnf(i_0_3250,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1675]) ).
cnf(i_0_3251,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1692]) ).
cnf(i_0_3252,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1405]) ).
cnf(i_0_3253,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X3,X2,esk8_4(X4,X3,X2,X1),X4) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oimage(X2,X3,X5,X1),X4)
| ~ c_Fun_Oinj__on(X2,X3,X5,X1) ),
inference(rename_variables,[],[i_0_1099]) ).
cnf(i_0_3254,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_3229,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604]) ).
cnf(i_0_3255,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(rename_variables,[],[i_0_2623]) ).
cnf(i_0_3256,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1604]) ).
cnf(i_0_3257,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_3229,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276]) ).
cnf(i_0_3258,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1276]) ).
cnf(i_0_3259,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_3229,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236]) ).
cnf(i_0_3260,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2150]) ).
cnf(i_0_3261,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1236]) ).
cnf(i_0_3262,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_3229,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237]) ).
cnf(i_0_3263,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(rename_variables,[],[i_0_1398]) ).
cnf(i_0_3264,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1237]) ).
cnf(i_0_3265,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3))),X4),X3),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299]) ).
cnf(i_0_3266,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)),X3),X2),
inference(rename_variables,[],[i_0_2652]) ).
cnf(i_0_3267,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1299]) ).
cnf(i_0_3268,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274]) ).
cnf(i_0_3269,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1274]) ).
cnf(i_0_3270,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450]) ).
cnf(i_0_3271,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2638]) ).
cnf(i_0_3272,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_3273,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1450]) ).
cnf(i_0_3274,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477]) ).
cnf(i_0_3275,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))),
inference(rename_variables,[],[i_0_2085]) ).
cnf(i_0_3276,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),X3) != c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_2686]) ).
cnf(i_0_3277,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1477]) ).
cnf(i_0_3278,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X4),X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238]) ).
cnf(i_0_3279,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)),X3),X4),X2),
inference(rename_variables,[],[i_0_2806]) ).
cnf(i_0_3280,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1238]) ).
cnf(i_0_3281,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368]) ).
cnf(i_0_3282,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_1736]) ).
cnf(i_0_3283,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(rename_variables,[],[i_0_1368]) ).
cnf(i_0_3284,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230]) ).
cnf(i_0_3285,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1230]) ).
cnf(i_0_3286,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231]) ).
cnf(i_0_3287,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1231]) ).
cnf(i_0_3288,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oinsert(X1,X2,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(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343]) ).
cnf(i_0_3289,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4) ),
inference(rename_variables,[],[i_0_1343]) ).
cnf(i_0_3290,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460]) ).
cnf(i_0_3291,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(rename_variables,[],[i_0_1460]) ).
cnf(i_0_3292,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),X2),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306]) ).
cnf(i_0_3293,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1306]) ).
cnf(i_0_3294,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,esk23_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306,i_0_1388]) ).
cnf(i_0_3295,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk27_2(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1388]) ).
cnf(i_0_3296,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306,i_0_1388,i_0_1443]) ).
cnf(i_0_3297,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1443]) ).
cnf(i_0_3298,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306,i_0_1388,i_0_1443,i_0_1444]) ).
cnf(i_0_3299,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1444]) ).
cnf(i_0_3300,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X3))),X3),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306,i_0_1388,i_0_1443,i_0_1444,i_0_1472]) ).
cnf(i_0_3301,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1472]) ).
cnf(i_0_3302,plain,
( c_member(X1,X2,c_Set_Oinsert(X1,X3,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X3,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2259,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306,i_0_1388,i_0_1443,i_0_1444,i_0_1472,i_0_1247]) ).
cnf(i_0_3303,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X4,X3))
| c_member(X1,X4,X2) ),
inference(rename_variables,[],[i_0_1247]) ).
cnf(i_0_3304,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2259,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_3243,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306,i_0_1388,i_0_1443,i_0_1444,i_0_1472,i_0_1247,i_0_1453]) ).
cnf(i_0_3305,plain,
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(rename_variables,[],[i_0_1591]) ).
cnf(i_0_3306,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 = X3 ),
inference(rename_variables,[],[i_0_1453]) ).
cnf(i_0_3307,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,esk9_4(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))),tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2259,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_3250,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_3243,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306,i_0_1388,i_0_1443,i_0_1444,i_0_1472,i_0_1247,i_0_1453,i_0_1129]) ).
cnf(i_0_3308,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1675]) ).
cnf(i_0_3309,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X3,X2,X4,X5) != X1
| c_Fun_Oinj__on(X2,X3,esk9_4(X5,X3,X2,X1),X1) ),
inference(rename_variables,[],[i_0_1129]) ).
cnf(i_0_3310,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,esk9_4(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))),tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),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(scs_inference,[],[i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2259,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_3250,i_0_3308,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_3243,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306,i_0_1388,i_0_1443,i_0_1444,i_0_1472,i_0_1247,i_0_1453,i_0_1129,i_0_1101]) ).
cnf(i_0_3311,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1675]) ).
cnf(i_0_3312,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oimage(X2,X3,esk9_4(X4,X3,X2,X1),X1),X4)
| c_Set_Oimage(X3,X2,X5,X4) != X1 ),
inference(rename_variables,[],[i_0_1101]) ).
cnf(i_0_3313,plain,
hAPP(esk9_4(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))),tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))) != hAPP(esk9_4(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))),tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_2138,i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2259,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_3250,i_0_3308,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_3243,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306,i_0_1388,i_0_1443,i_0_1444,i_0_1472,i_0_1247,i_0_1453,i_0_1129,i_0_1101,i_0_1216]) ).
cnf(i_0_3314,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| hAPP(X3,X4) != hAPP(X3,X5)
| X4 = X5 ),
inference(rename_variables,[],[i_0_1216]) ).
cnf(i_0_3315,plain,
( c_member(X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X2),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Set_Oinsert(X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(scs_inference,[],[i_0_2138,i_0_2780,i_0_2646,i_0_2834,i_0_2569,i_0_2536,i_0_2573,i_0_2996,i_0_2998,i_0_3147,i_0_3149,i_0_3151,i_0_3153,i_0_3155,i_0_3157,i_0_3159,i_0_3161,i_0_3163,i_0_3165,i_0_3167,i_0_3169,i_0_3171,i_0_3173,i_0_3175,i_0_3177,i_0_3179,i_0_3181,i_0_3183,i_0_3185,i_0_3193,i_0_3196,i_0_2686,i_0_3065,i_0_2566,i_0_2003,i_0_3191,i_0_3204,i_0_2313,i_0_2150,i_0_3135,i_0_3235,i_0_3260,i_0_2159,i_0_3060,i_0_2347,i_0_2179,i_0_3098,i_0_2214,i_0_3210,i_0_2222,i_0_2195,i_0_2745,i_0_2731,i_0_2725,i_0_2723,i_0_2721,i_0_2717,i_0_2715,i_0_2713,i_0_2711,i_0_2709,i_0_2707,i_0_2705,i_0_2703,i_0_2701,i_0_2699,i_0_2697,i_0_2695,i_0_2595,i_0_2625,i_0_3216,i_0_2627,i_0_2693,i_0_2623,i_0_3222,i_0_2161,i_0_2733,i_0_3187,i_0_2787,i_0_2896,i_0_2946,i_0_2503,i_0_3000,i_0_3003,i_0_2537,i_0_2852,i_0_2882,i_0_2885,i_0_2691,i_0_2424,i_0_2729,i_0_2006,i_0_2478,i_0_2737,i_0_2741,i_0_2689,i_0_2743,i_0_2727,i_0_2719,i_0_2169,i_0_2652,i_0_2859,i_0_2890,i_0_2918,i_0_2937,i_0_2952,i_0_2960,i_0_2969,i_0_3107,i_0_2749,i_0_2192,i_0_2220,i_0_2187,i_0_2186,i_0_1795,i_0_2085,i_0_2963,i_0_2986,i_0_3113,i_0_2353,i_0_2966,i_0_1543,i_0_1582,i_0_2300,i_0_2327,i_0_1692,i_0_3229,i_0_1690,i_0_1788,i_0_2340,i_0_2079,i_0_2915,i_0_1677,i_0_1398,i_0_3247,i_0_1731,i_0_3022,i_0_3047,i_0_3189,i_0_3200,i_0_3202,i_0_3208,i_0_2031,i_0_2259,i_0_2232,i_0_2320,i_0_2051,i_0_2329,i_0_1768,i_0_2125,i_0_1430,i_0_2893,i_0_1694,i_0_1592,i_0_1802,i_0_1469,i_0_3053,i_0_3073,i_0_2446,i_0_3221,i_0_2398,i_0_2856,i_0_2816,i_0_2529,i_0_2548,i_0_2642,i_0_2666,i_0_2406,i_0_2923,i_0_2239,i_0_2422,i_0_3061,i_0_2814,i_0_2483,i_0_2416,i_0_2611,i_0_2638,i_0_2867,i_0_3246,i_0_2455,i_0_2681,i_0_2796,i_0_2799,i_0_2656,i_0_2500,i_0_2512,i_0_2523,i_0_2458,i_0_2806,i_0_2485,i_0_2669,i_0_2493,i_0_2673,i_0_1675,i_0_3250,i_0_3308,i_0_1335,i_0_2023,i_0_2034,i_0_2136,i_0_1791,i_0_1405,i_0_3230,i_0_1591,i_0_3243,i_0_1736,i_0_3125,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1779,i_0_1792,i_0_1828,i_0_1878,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1728,i_0_1304,i_0_1088,i_0_1114,i_0_1125,i_0_1588,i_0_1632,i_0_1633,i_0_1725,i_0_1410,i_0_1417,i_0_1665,i_0_1680,i_0_1714,i_0_1724,i_0_1760,i_0_1673,i_0_1115,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1170,i_0_1333,i_0_1414,i_0_1416,i_0_1507,i_0_1535,i_0_1635,i_0_1674,i_0_1734,i_0_1429,i_0_1539,i_0_1590,i_0_1661,i_0_1664,i_0_1689,i_0_1352,i_0_1447,i_0_1537,i_0_1270,i_0_1660,i_0_1510,i_0_1574,i_0_1581,i_0_1691,i_0_1351,i_0_1473,i_0_1511,i_0_1512,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1645,i_0_1715,i_0_1290,i_0_1286,i_0_1222,i_0_1124,i_0_1289,i_0_1644,i_0_1285,i_0_1288,i_0_1226,i_0_1284,i_0_1224,i_0_1515,i_0_1400,i_0_1651,i_0_1653,i_0_1135,i_0_1197,i_0_1382,i_0_1451,i_0_1693,i_0_1496,i_0_1089,i_0_1149,i_0_1541,i_0_1583,i_0_1654,i_0_1655,i_0_1719,i_0_1720,i_0_1721,i_0_1220,i_0_1174,i_0_1702,i_0_1436,i_0_1486,i_0_1478,i_0_1345,i_0_1618,i_0_1246,i_0_1287,i_0_1494,i_0_1556,i_0_1485,i_0_1573,i_0_1283,i_0_1620,i_0_1493,i_0_1401,i_0_1245,i_0_1558,i_0_1489,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1923,i_0_1929,i_0_1936,i_0_1937,i_0_1892,i_0_1920,i_0_1921,i_0_1926,i_0_1930,i_0_1935,i_0_1931,i_0_1925,i_0_1927,i_0_1928,i_0_1924,i_0_1423,i_0_1235,i_0_1298,i_0_1300,i_0_1095,i_0_1422,i_0_1424,i_0_1425,i_0_1428,i_0_1356,i_0_1613,i_0_1099,i_0_1604,i_0_1276,i_0_1236,i_0_1237,i_0_1299,i_0_1274,i_0_1450,i_0_1477,i_0_1238,i_0_1368,i_0_1230,i_0_1231,i_0_1343,i_0_1460,i_0_1306,i_0_1388,i_0_1443,i_0_1444,i_0_1472,i_0_1247,i_0_1453,i_0_1129,i_0_1101,i_0_1216,i_0_1339]) ).
cnf(i_0_3316,plain,
( ~ c_member(X1,X2,c_Set_Oinsert(X1,X3,X4))
| X2 = X3
| c_member(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1339]) ).
cnf(i_0_3317,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),c_Set_Oimage(X3,X2,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_2214]) ).
cnf(i_0_3318,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(rename_variables,[],[i_0_2179]) ).
cnf(i_0_3319,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2150]) ).
cnf(i_0_3320,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))),
inference(rename_variables,[],[i_0_2085]) ).
cnf(i_0_3322,plain,
c_Fun_Oinj__on(X1,X2,X3,c_Set_Oimage(X4,X1,X5,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2879,i_0_1171]) ).
cnf(i_0_3323,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_2879]) ).
cnf(i_0_3324,plain,
( c_member(X1,esk2_4(X2,X3,X4,X1),X2)
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(rename_variables,[],[i_0_1171]) ).
cnf(i_0_3325,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X4)),X1),
inference(scs_inference,[],[i_0_2664,i_0_2879,i_0_1171,i_0_1303]) ).
cnf(i_0_3326,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),X4),X1),
inference(rename_variables,[],[i_0_2664]) ).
cnf(i_0_3327,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1303]) ).
cnf(i_0_3328,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),X2),
inference(scs_inference,[],[i_0_2664,i_0_2879,i_0_3259,i_0_1171,i_0_1303,i_0_1305]) ).
cnf(i_0_3329,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),
inference(rename_variables,[],[i_0_3259]) ).
cnf(i_0_3330,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1305]) ).
cnf(i_0_3331,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_Nat_OSuc,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2664,i_0_2483,i_0_2879,i_0_3259,i_0_1171,i_0_1303,i_0_1305,i_0_1687]) ).
cnf(i_0_3332,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(rename_variables,[],[i_0_1687]) ).
cnf(i_0_3333,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X3),
inference(scs_inference,[],[i_0_2664,i_0_2483,i_0_2879,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304]) ).
cnf(i_0_3334,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X3),
inference(rename_variables,[],[i_0_3105]) ).
cnf(i_0_3335,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1304]) ).
cnf(i_0_3336,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2),
inference(scs_inference,[],[i_0_2664,i_0_2483,i_0_2879,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306]) ).
cnf(i_0_3337,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1306]) ).
cnf(i_0_3338,plain,
X1 != hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(scs_inference,[],[i_0_2907,i_0_2664,i_0_2483,i_0_2879,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828]) ).
cnf(i_0_3339,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)),
inference(rename_variables,[],[i_0_2907]) ).
cnf(i_0_3340,plain,
c_Finite__Set_Ocard(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2907,i_0_1730,i_0_2664,i_0_2483,i_0_2879,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725]) ).
cnf(i_0_3341,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_3342,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1725]) ).
cnf(i_0_3343,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X1,X4,X3,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4),X2),
inference(scs_inference,[],[i_0_2907,i_0_1730,i_0_2664,i_0_2483,i_0_2879,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088]) ).
cnf(i_0_3344,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X3,X1,X4,X5))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),esk19_5(X5,X4,X3,X2,X1),X5) ),
inference(rename_variables,[],[i_0_1088]) ).
cnf(i_0_3345,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Set_Oimage(X5,X3,X6,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),
inference(scs_inference,[],[i_0_2907,i_0_1730,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114]) ).
cnf(i_0_3346,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_2879]) ).
cnf(i_0_3347,plain,
( c_member(X1,esk18_4(X2,X3,X1,X4),X2)
| ~ c_member(X5,X4,c_Set_Oimage(X1,X5,X3,X2)) ),
inference(rename_variables,[],[i_0_1114]) ).
cnf(i_0_3348,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,esk19_5(X4,X5,X2,esk19_5(c_Set_Oimage(X2,X6,X5,X4),X7,X6,c_Set_Oimage(X6,X8,X7,c_Set_Oimage(X2,X6,X5,X4)),X8),X6)),c_Set_Oimage(X2,X1,X3,X4)),
inference(scs_inference,[],[i_0_2907,i_0_1730,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125]) ).
cnf(i_0_3349,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2),c_Set_Oimage(X1,X4,X5,X3)) ),
inference(rename_variables,[],[i_0_1125]) ).
cnf(i_0_3350,plain,
c_member(X1,esk17_2(hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X1),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2907,i_0_2851,i_0_1730,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632]) ).
cnf(i_0_3351,plain,
hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X2,
inference(rename_variables,[],[i_0_2851]) ).
cnf(i_0_3352,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_member(X2,esk17_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_1632]) ).
cnf(i_0_3353,plain,
c_member(X1,esk16_2(hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X1),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2907,i_0_2851,i_0_3351,i_0_1730,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633]) ).
cnf(i_0_3354,plain,
hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X2,
inference(rename_variables,[],[i_0_2851]) ).
cnf(i_0_3355,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_member(X2,esk16_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_1633]) ).
cnf(i_0_3356,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X3)) != X1,
inference(scs_inference,[],[i_0_2959,i_0_2907,i_0_2851,i_0_3351,i_0_1730,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665]) ).
cnf(i_0_3357,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X3) != X2,
inference(rename_variables,[],[i_0_2959]) ).
cnf(i_0_3358,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
inference(rename_variables,[],[i_0_1665]) ).
cnf(i_0_3359,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1),
inference(scs_inference,[],[i_0_2959,i_0_2907,i_0_2851,i_0_3351,i_0_3102,i_0_1730,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410]) ).
cnf(i_0_3360,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3102]) ).
cnf(i_0_3361,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1410]) ).
cnf(i_0_3362,plain,
~ c_member(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2959,i_0_2907,i_0_2851,i_0_3351,i_0_3102,i_0_1730,i_0_3341,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588]) ).
cnf(i_0_3363,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_3364,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_member(X2,X3,X1) ),
inference(rename_variables,[],[i_0_1588]) ).
cnf(i_0_3365,plain,
c_Orderings_Oord__class_Oless__eq(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1,X1),
inference(scs_inference,[],[i_0_2959,i_0_2907,i_0_2851,i_0_3351,i_0_3164,i_0_3102,i_0_1730,i_0_3341,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724]) ).
cnf(i_0_3366,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(rename_variables,[],[i_0_1724]) ).
cnf(i_0_3367,plain,
c_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(scs_inference,[],[i_0_2959,i_0_2907,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_1730,i_0_3341,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760]) ).
cnf(i_0_3368,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_3369,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2959,i_0_2907,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_1730,i_0_3341,i_0_3363,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332]) ).
cnf(i_0_3370,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_3371,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = c_Set_Oimage(X2,X3,X4,X1) ),
inference(rename_variables,[],[i_0_1332]) ).
cnf(i_0_3372,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))),
inference(scs_inference,[],[i_0_2959,i_0_2907,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_2076,i_0_1730,i_0_3341,i_0_3363,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348]) ).
cnf(i_0_3373,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_2076]) ).
cnf(i_0_3374,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1348]) ).
cnf(i_0_3375,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X2),
inference(scs_inference,[],[i_0_2171,i_0_2959,i_0_2907,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_2076,i_0_1730,i_0_3341,i_0_3363,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412]) ).
cnf(i_0_3376,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),X1),
inference(rename_variables,[],[i_0_2171]) ).
cnf(i_0_3377,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1412]) ).
cnf(i_0_3378,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2171,i_0_2959,i_0_2907,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_2076,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506]) ).
cnf(i_0_3379,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_3380,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1)) ),
inference(rename_variables,[],[i_0_1506]) ).
cnf(i_0_3381,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_2076,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673]) ).
cnf(i_0_3382,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_1673]) ).
cnf(i_0_3383,plain,
~ c_member(X1,esk23_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Set_Oimage(X2,X1,c_Nat_OSuc,X3)),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_2076,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115]) ).
cnf(i_0_3384,plain,
esk23_2(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(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_2983]) ).
cnf(i_0_3385,plain,
( X1 = hAPP(X2,esk18_4(X3,X2,X4,X1))
| ~ c_member(X5,X1,c_Set_Oimage(X4,X5,X2,X3)) ),
inference(rename_variables,[],[i_0_1115]) ).
cnf(i_0_3386,plain,
c_Set_Oimage(X1,X2,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_2076,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333]) ).
cnf(i_0_3387,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_3388,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X2,X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_1333]) ).
cnf(i_0_3389,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X1),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_2092,i_0_2076,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414]) ).
cnf(i_0_3390,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X1),
inference(rename_variables,[],[i_0_2092]) ).
cnf(i_0_3391,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1414]) ).
cnf(i_0_3392,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_2092,i_0_2076,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417]) ).
cnf(i_0_3393,plain,
( X1 != hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1417]) ).
cnf(i_0_3394,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507]) ).
cnf(i_0_3395,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_2076]) ).
cnf(i_0_3396,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1507]) ).
cnf(i_0_3397,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_3360,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535]) ).
cnf(i_0_3398,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3102]) ).
cnf(i_0_3399,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1535]) ).
cnf(i_0_3400,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_3360,i_0_2809,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680]) ).
cnf(i_0_3401,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(rename_variables,[],[i_0_1680]) ).
cnf(i_0_3402,plain,
c_Fun_Oinj__on(tc_Nat_Onat,X1,X2,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_3360,i_0_2809,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170]) ).
cnf(i_0_3403,plain,
~ c_member(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_3227]) ).
cnf(i_0_3404,plain,
( c_member(X1,esk3_4(X2,X3,X4,X1),X2)
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(rename_variables,[],[i_0_1170]) ).
cnf(i_0_3405,plain,
esk4_4(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) != X1,
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_3360,i_0_3398,i_0_2809,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689]) ).
cnf(i_0_3406,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3102]) ).
cnf(i_0_3407,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1689]) ).
cnf(i_0_3408,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3))),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_3360,i_0_3398,i_0_2098,i_0_2809,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352]) ).
cnf(i_0_3409,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(rename_variables,[],[i_0_2098]) ).
cnf(i_0_3410,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_1352]) ).
cnf(i_0_3411,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_2098,i_0_2809,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537]) ).
cnf(i_0_3412,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3102]) ).
cnf(i_0_3413,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1537]) ).
cnf(i_0_3414,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Set_Oimage(X1,X2,esk8_4(c_Set_Oinsert(X1,X3,X4),X1,X2,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X1,X3,X4)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_2098,i_0_2809,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635]) ).
cnf(i_0_3415,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1635]) ).
cnf(i_0_3416,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_2098,i_0_2809,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661]) ).
cnf(i_0_3417,plain,
~ c_member(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_3227]) ).
cnf(i_0_3418,plain,
( c_member(tc_Nat_Onat,esk13_2(X1,X2),X1)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(rename_variables,[],[i_0_1661]) ).
cnf(i_0_3419,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_2098,i_0_2809,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664]) ).
cnf(i_0_3420,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1664]) ).
cnf(i_0_3421,plain,
hAPP(c_Nat_OSuc,X1) != c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_2098,i_0_2809,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734]) ).
cnf(i_0_3422,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_1734]) ).
cnf(i_0_3423,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X3),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_2098,i_0_2809,i_0_2054,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416]) ).
cnf(i_0_3424,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X2),
inference(rename_variables,[],[i_0_2054]) ).
cnf(i_0_3425,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1416]) ).
cnf(i_0_3426,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_2098,i_0_2809,i_0_2054,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429]) ).
cnf(i_0_3427,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X3) != X2,
inference(rename_variables,[],[i_0_2959]) ).
cnf(i_0_3428,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
inference(rename_variables,[],[i_0_1429]) ).
cnf(i_0_3429,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))),X2),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_2098,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447]) ).
cnf(i_0_3430,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(rename_variables,[],[i_0_2291]) ).
cnf(i_0_3431,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1447]) ).
cnf(i_0_3432,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,esk4_4(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_2076,i_0_3373,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590]) ).
cnf(i_0_3433,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3102]) ).
cnf(i_0_3434,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1590]) ).
cnf(i_0_3435,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674]) ).
cnf(i_0_3436,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(rename_variables,[],[i_0_1674]) ).
cnf(i_0_3437,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2))),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511]) ).
cnf(i_0_3438,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(rename_variables,[],[i_0_2098]) ).
cnf(i_0_3439,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1511]) ).
cnf(i_0_3440,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X1),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539]) ).
cnf(i_0_3441,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X1),
inference(rename_variables,[],[i_0_2092]) ).
cnf(i_0_3442,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1539]) ).
cnf(i_0_3443,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != hAPP(c_Nat_OSuc,X1),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691]) ).
cnf(i_0_3444,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(rename_variables,[],[i_0_1691]) ).
cnf(i_0_3445,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,hAPP(c_Nat_OSuc,c_Set_Oimage(X4,X1,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270]) ).
cnf(i_0_3446,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2),X3) ),
inference(rename_variables,[],[i_0_1270]) ).
cnf(i_0_3447,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(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(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660]) ).
cnf(i_0_3448,plain,
( c_member(tc_Nat_Onat,esk15_2(X1,X2),X1)
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(rename_variables,[],[i_0_1660]) ).
cnf(i_0_3449,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3))),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351]) ).
cnf(i_0_3450,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(rename_variables,[],[i_0_2098]) ).
cnf(i_0_3451,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_1351]) ).
cnf(i_0_3452,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2))),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510]) ).
cnf(i_0_3453,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(rename_variables,[],[i_0_2098]) ).
cnf(i_0_3454,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1510]) ).
cnf(i_0_3455,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Onat_Onat__size(X1),c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574]) ).
cnf(i_0_3456,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1574]) ).
cnf(i_0_3457,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X3)),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2470,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581]) ).
cnf(i_0_3458,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1581]) ).
cnf(i_0_3459,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X3))),X3),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2470,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473]) ).
cnf(i_0_3460,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1473]) ).
cnf(i_0_3461,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512]) ).
cnf(i_0_3462,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1512]) ).
cnf(i_0_3463,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2)),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444]) ).
cnf(i_0_3464,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1444]) ).
cnf(i_0_3465,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,X3))),X3),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472]) ).
cnf(i_0_3466,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3))),X3),
inference(rename_variables,[],[i_0_3218]) ).
cnf(i_0_3467,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1472]) ).
cnf(i_0_3468,plain,
c_Arrow__Order__Mirabelle_Ounanimity(esk4_4(hAPP(c_Nat_OSuc,v_F),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375]) ).
cnf(i_0_3469,plain,
X1 = esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),
inference(rename_variables,[],[i_0_2181]) ).
cnf(i_0_3470,plain,
c_Arrow__Order__Mirabelle_OIIA(esk4_4(hAPP(c_Nat_OSuc,v_F),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376]) ).
cnf(i_0_3471,plain,
X1 = esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),
inference(rename_variables,[],[i_0_2181]) ).
cnf(i_0_3472,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)))) != X2,
inference(scs_inference,[],[i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_3427,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827]) ).
cnf(i_0_3473,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X3) != X2,
inference(rename_variables,[],[i_0_2959]) ).
cnf(i_0_3474,plain,
c_Set_Oimage(X1,X2,X3,c_Set_Oinsert(X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) = c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_3039,i_0_3037,i_0_3063,i_0_2171,i_0_2959,i_0_3357,i_0_3427,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806]) ).
cnf(i_0_3475,plain,
c_Orderings_Oord__class_Oless__eq(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1,X1),
inference(scs_inference,[],[i_0_3039,i_0_3037,i_0_3063,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377]) ).
cnf(i_0_3476,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1692]) ).
cnf(i_0_3477,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X1,X2),c_SetInterval_Oord__class_OgreaterThan(X1,X3))
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1377]) ).
cnf(i_0_3478,plain,
~ c_member(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk14_1(c_Set_Oinsert(tc_Nat_Onat,hAPP(X1,X2),c_Set_Oimage(tc_Product__Type_Ounit,tc_Nat_Onat,X1,X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Set_Oinsert(tc_Nat_Onat,hAPP(X1,X2),c_Set_Oimage(tc_Product__Type_Ounit,tc_Nat_Onat,X1,X3))),
inference(scs_inference,[],[i_0_3039,i_0_3037,i_0_3063,i_0_2313,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527]) ).
cnf(i_0_3479,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(rename_variables,[],[i_0_2313]) ).
cnf(i_0_3480,plain,
c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4))),
inference(rename_variables,[],[i_0_2548]) ).
cnf(i_0_3481,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk14_1(X2))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2)
| ~ c_member(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1527]) ).
cnf(i_0_3482,plain,
~ c_member(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk12_1(c_Set_Oinsert(tc_Nat_Onat,hAPP(X1,X2),c_Set_Oimage(tc_Product__Type_Ounit,tc_Nat_Onat,X1,X3)))),X4),X5),c_Set_Oinsert(tc_Nat_Onat,hAPP(X1,X2),c_Set_Oimage(tc_Product__Type_Ounit,tc_Nat_Onat,X1,X3))),
inference(scs_inference,[],[i_0_3039,i_0_3037,i_0_3063,i_0_2313,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526]) ).
cnf(i_0_3483,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2164]) ).
cnf(i_0_3484,plain,
c_Finite__Set_Ofinite(X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4))),
inference(rename_variables,[],[i_0_2548]) ).
cnf(i_0_3485,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,esk12_1(X2))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2)
| ~ c_member(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1526]) ).
cnf(i_0_3486,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_3039,i_0_3037,i_0_3063,i_0_2313,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645]) ).
cnf(i_0_3487,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X3) != X2,
inference(rename_variables,[],[i_0_2959]) ).
cnf(i_0_3488,plain,
( 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(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3489,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_3039,i_0_3037,i_0_3063,i_0_2313,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715]) ).
cnf(i_0_3490,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X3) != X2,
inference(rename_variables,[],[i_0_2959]) ).
cnf(i_0_3491,plain,
( 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(rename_variables,[],[i_0_1715]) ).
cnf(i_0_3492,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X3),
inference(scs_inference,[],[i_0_3039,i_0_3037,i_0_3063,i_0_2313,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290]) ).
cnf(i_0_3493,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_1290]) ).
cnf(i_0_3494,plain,
c_Finite__Set_Ofinite(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124]) ).
cnf(i_0_3495,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X1,tc_Nat_Onat,X2,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_2973]) ).
cnf(i_0_3496,plain,
c_Fun_Oinj__on(X1,X2,X3,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_2448]) ).
cnf(i_0_3497,plain,
( ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,X4))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4)
| c_Finite__Set_Ofinite(X2,X4) ),
inference(rename_variables,[],[i_0_1124]) ).
cnf(i_0_3498,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(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(scs_inference,[],[i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644]) ).
cnf(i_0_3499,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = 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))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1644]) ).
cnf(i_0_3500,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)))),X3),
inference(scs_inference,[],[i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3259,i_0_3265,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288]) ).
cnf(i_0_3501,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3))),X4),X3),
inference(rename_variables,[],[i_0_3265]) ).
cnf(i_0_3502,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_1288]) ).
cnf(i_0_3503,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),
inference(scs_inference,[],[i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284]) ).
cnf(i_0_3504,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3),X2),
inference(rename_variables,[],[i_0_2869]) ).
cnf(i_0_3505,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_1284]) ).
cnf(i_0_3506,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X4)))),
inference(scs_inference,[],[i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224]) ).
cnf(i_0_3507,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)),X4)),
inference(rename_variables,[],[i_0_3029]) ).
cnf(i_0_3508,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1224]) ).
cnf(i_0_3509,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X3)),
inference(scs_inference,[],[i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631]) ).
cnf(i_0_3510,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X3),X1),
inference(rename_variables,[],[i_0_3127]) ).
cnf(i_0_3511,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1631]) ).
cnf(i_0_3512,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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(scs_inference,[],[i_0_2784,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651]) ).
cnf(i_0_3513,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1651]) ).
cnf(i_0_3514,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653]) ).
cnf(i_0_3515,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1653]) ).
cnf(i_0_3516,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5)),c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5))),
inference(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135]) ).
cnf(i_0_3517,plain,
c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5)) = c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5)),
inference(rename_variables,[],[i_0_3001]) ).
cnf(i_0_3518,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1692]) ).
cnf(i_0_3519,plain,
( X1 != c_Set_Oimage(X2,X3,X4,X5)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oimage(X2,X3,X4,X6))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X5,X6) ),
inference(rename_variables,[],[i_0_1135]) ).
cnf(i_0_3520,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451]) ).
cnf(i_0_3521,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_2076]) ).
cnf(i_0_3522,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(X2,X1),X2) ),
inference(rename_variables,[],[i_0_1451]) ).
cnf(i_0_3523,plain,
c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,c_Set_Oinsert(X2,hAPP(X4,X5),c_Set_Oimage(tc_Product__Type_Ounit,X2,X4,X6)))),
inference(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149]) ).
cnf(i_0_3524,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1692]) ).
cnf(i_0_3525,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X3,X1,X4,X5))
| c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X5) ),
inference(rename_variables,[],[i_0_1149]) ).
cnf(i_0_3526,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197]) ).
cnf(i_0_3527,plain,
hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X2,
inference(rename_variables,[],[i_0_2851]) ).
cnf(i_0_3528,plain,
hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X1,
inference(rename_variables,[],[i_0_2006]) ).
cnf(i_0_3529,plain,
( X1 = c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_3530,plain,
c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693]) ).
cnf(i_0_3531,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1600]) ).
cnf(i_0_3532,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_1693]) ).
cnf(i_0_3533,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720]) ).
cnf(i_0_3534,plain,
( ~ class_Orderings_Opreorder(X1)
| X2 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1720]) ).
cnf(i_0_3535,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4)))),
inference(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583]) ).
cnf(i_0_3536,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1600]) ).
cnf(i_0_3537,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_1583]) ).
cnf(i_0_3538,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400]) ).
cnf(i_0_3539,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rename_variables,[],[i_0_3242]) ).
cnf(i_0_3540,plain,
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(rename_variables,[],[i_0_1591]) ).
cnf(i_0_3541,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2)
| X2 = X3 ),
inference(rename_variables,[],[i_0_1400]) ).
cnf(i_0_3542,plain,
~ c_Orderings_Oord__class_Oless(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654]) ).
cnf(i_0_3543,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1654]) ).
cnf(i_0_3544,plain,
~ c_Orderings_Oord__class_Oless(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655]) ).
cnf(i_0_3545,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1655]) ).
cnf(i_0_3546,plain,
~ c_member(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk19_5(c_Set_Oimage(X2,X1,c_Nat_OSuc,X3),X4,X1,esk19_5(c_Set_Oimage(X1,X5,X4,c_Set_Oimage(X2,X1,c_Nat_OSuc,X3)),X6,X5,c_Set_Oimage(X5,X7,X6,c_Set_Oimage(X1,X5,X4,c_Set_Oimage(X2,X1,c_Nat_OSuc,X3))),X7),X5)),
inference(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382]) ).
cnf(i_0_3547,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk19_5(X2,X3,X1,esk19_5(c_Set_Oimage(X1,X4,X3,X2),X5,X4,c_Set_Oimage(X4,X6,X5,c_Set_Oimage(X1,X4,X3,X2)),X6),X4),X2),
inference(rename_variables,[],[i_0_2395]) ).
cnf(i_0_3548,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_member(X1,X4,X2)
| c_member(X1,X4,X3) ),
inference(rename_variables,[],[i_0_1382]) ).
cnf(i_0_3549,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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(scs_inference,[],[i_0_2784,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719]) ).
cnf(i_0_3550,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1719]) ).
cnf(i_0_3551,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721]) ).
cnf(i_0_3552,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X1,X2) ),
inference(rename_variables,[],[i_0_1721]) ).
cnf(i_0_3553,plain,
~ c_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_1592,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541]) ).
cnf(i_0_3554,plain,
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_1592]) ).
cnf(i_0_3555,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(rename_variables,[],[i_0_1541]) ).
cnf(i_0_3556,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2413,i_0_1592,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436]) ).
cnf(i_0_3557,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(rename_variables,[],[i_0_2313]) ).
cnf(i_0_3558,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(rename_variables,[],[i_0_1436]) ).
cnf(i_0_3559,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2413,i_0_1592,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220]) ).
cnf(i_0_3560,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3)),
inference(rename_variables,[],[i_0_2602]) ).
cnf(i_0_3561,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1220]) ).
cnf(i_0_3562,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,esk9_4(c_Set_Oinsert(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Set_Oinsert(tc_Nat_Onat,X2,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))),tc_Nat_Onat,tc_Nat_Onat,c_Set_Oinsert(tc_Nat_Onat,X2,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),X3),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174]) ).
cnf(i_0_3563,plain,
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_1592]) ).
cnf(i_0_3564,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,esk9_4(c_Set_Oinsert(tc_Nat_Onat,X1,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Set_Oinsert(tc_Nat_Onat,X2,X3))),tc_Nat_Onat,tc_Nat_Onat,c_Set_Oinsert(tc_Nat_Onat,X2,X3)),X3),
inference(rename_variables,[],[i_0_3092]) ).
cnf(i_0_3565,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| c_Fun_Oinj__on(X1,X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
inference(rename_variables,[],[i_0_1174]) ).
cnf(i_0_3566,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478]) ).
cnf(i_0_3567,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X1),
inference(rename_variables,[],[i_0_2276]) ).
cnf(i_0_3568,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2232]) ).
cnf(i_0_3569,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != hAPP(c_Nat_OSuc,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_1478]) ).
cnf(i_0_3570,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Set_Oimage(X1,X2,esk8_4(c_Set_Oinsert(X1,X3,X4),X1,X2,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4))),c_Set_Oinsert(X1,X3,X4)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oinsert(X2,hAPP(X5,X3),c_Set_Oimage(X1,X2,X5,X4)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618]) ).
cnf(i_0_3571,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1618]) ).
cnf(i_0_3572,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702]) ).
cnf(i_0_3573,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(rename_variables,[],[i_0_1702]) ).
cnf(i_0_3574,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494]) ).
cnf(i_0_3575,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1494]) ).
cnf(i_0_3576,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X3),X1),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_2515,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287]) ).
cnf(i_0_3577,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X2),X3),X1),
inference(rename_variables,[],[i_0_2515]) ).
cnf(i_0_3578,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1287]) ).
cnf(i_0_3579,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Set_Othe__elem(X1,c_Set_Oinsert(X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_2515,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486]) ).
cnf(i_0_3580,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1486]) ).
cnf(i_0_3581,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))),X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246]) ).
cnf(i_0_3582,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X3),X2),
inference(rename_variables,[],[i_0_2968]) ).
cnf(i_0_3583,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4) ),
inference(rename_variables,[],[i_0_1246]) ).
cnf(i_0_3584,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Set_Othe__elem(X2,c_Set_Oinsert(X2,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3029,i_0_2869,i_0_3259,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556]) ).
cnf(i_0_3585,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1556]) ).
cnf(i_0_3586,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X4))),X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283]) ).
cnf(i_0_3587,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X4),X2),
inference(rename_variables,[],[i_0_2889]) ).
cnf(i_0_3588,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1283]) ).
cnf(i_0_3589,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620]) ).
cnf(i_0_3590,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1620]) ).
cnf(i_0_3591,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk23_2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485]) ).
cnf(i_0_3592,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1485]) ).
cnf(i_0_3593,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X3)),X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245]) ).
cnf(i_0_3594,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2150]) ).
cnf(i_0_3595,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4) ),
inference(rename_variables,[],[i_0_1245]) ).
cnf(i_0_3596,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2))),X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493]) ).
cnf(i_0_3597,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1493]) ).
cnf(i_0_3598,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5)),c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489]) ).
cnf(i_0_3599,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1489]) ).
cnf(i_0_3600,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk23_2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558]) ).
cnf(i_0_3601,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_3602,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573]) ).
cnf(i_0_3603,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_1736]) ).
cnf(i_0_3604,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1573]) ).
cnf(i_0_3605,plain,
tc_HOL_Obool != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915]) ).
cnf(i_0_3606,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Set_Oinsert(tc_Nat_Onat,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) != 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(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807]) ).
cnf(i_0_3607,plain,
c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Set_Oimage(X1,X2,X3,c_Set_Oinsert(X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_3039]) ).
cnf(i_0_3608,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_2138]) ).
cnf(i_0_3609,plain,
class_Orderings_Oorder(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894]) ).
cnf(i_0_3610,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3611,plain,
class_Orderings_Olinorder(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895]) ).
cnf(i_0_3612,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3613,plain,
class_Rings_Ocomm__semiring__1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896]) ).
cnf(i_0_3614,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3615,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897]) ).
cnf(i_0_3616,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3617,plain,
class_Groups_Oordered__ab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898]) ).
cnf(i_0_3618,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3619,plain,
class_Groups_Ocomm__monoid__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900]) ).
cnf(i_0_3620,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3621,plain,
class_Groups_Oordered__comm__monoid__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904]) ).
cnf(i_0_3622,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3623,plain,
class_Rings_Olinordered__semidom(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906]) ).
cnf(i_0_3624,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3625,plain,
class_Groups_Oab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908]) ).
cnf(i_0_3626,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3627,plain,
class_Orderings_Opreorder(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909]) ).
cnf(i_0_3628,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3629,plain,
class_Groups_Ocancel__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910]) ).
cnf(i_0_3630,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3631,plain,
class_Groups_Ocancel__ab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911]) ).
cnf(i_0_3632,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3633,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912]) ).
cnf(i_0_3634,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3635,plain,
class_Orderings_Oord(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913]) ).
cnf(i_0_3636,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3637,plain,
class_Orderings_Obot(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914]) ).
cnf(i_0_3638,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3639,plain,
class_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916]) ).
cnf(i_0_3640,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3641,plain,
class_Groups_Omonoid__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917]) ).
cnf(i_0_3642,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3643,plain,
class_Rings_Ozero__neq__one(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918]) ).
cnf(i_0_3644,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3645,plain,
class_Groups_Oone(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919]) ).
cnf(i_0_3646,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3647,plain,
class_Groups_Ozero(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922]) ).
cnf(i_0_3648,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3649,plain,
~ c_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,esk8_4(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))),tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),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(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936]) ).
cnf(i_0_3650,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937]) ).
cnf(i_0_3651,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3652,plain,
c_Arrow__Order__Mirabelle_Ounanimity(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,v_F)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920]) ).
cnf(i_0_3653,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3654,plain,
c_Arrow__Order__Mirabelle_OIIA(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,v_F)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921]) ).
cnf(i_0_3655,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_2573]) ).
cnf(i_0_3656,plain,
~ c_member(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Nat_OSuc,X2)),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923]) ).
cnf(i_0_3657,plain,
~ c_member(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Set_Oimage(X2,X1,c_Nat_OSuc,X3)),
inference(rename_variables,[],[i_0_2208]) ).
cnf(i_0_3658,plain,
~ c_Orderings_Oord__class_Oless(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),tc_fun(X1,tc_HOL_Obool)),X2,X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_1976,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926]) ).
cnf(i_0_3659,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_3660,plain,
~ c_Orderings_Oord__class_Oless__eq(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),tc_Nat_Onat),hAPP(c_Nat_OSuc,X1),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_2175,i_0_1976,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929]) ).
cnf(i_0_3661,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_3662,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3039,i_0_2448,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930]) ).
cnf(i_0_3663,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(rename_variables,[],[i_0_2313]) ).
cnf(i_0_3664,plain,
hAPP(c_Nat_OSuc,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_1711]) ).
cnf(i_0_3665,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931]) ).
cnf(i_0_3666,plain,
~ c_Finite__Set_Ofinite(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935]) ).
cnf(i_0_3667,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_3668,plain,
~ c_member(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1627,i_0_1591,i_0_1736,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925]) ).
cnf(i_0_3669,plain,
~ c_member(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X2,c_Set_Oinsert(X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Nat_OSuc,X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_3207]) ).
cnf(i_0_3670,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3304]) ).
cnf(i_0_3671,plain,
c_fTrue != c_fFalse,
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892]) ).
cnf(i_0_3672,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927]) ).
cnf(i_0_3673,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1976]) ).
cnf(i_0_3674,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_3673,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928]) ).
cnf(i_0_3675,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1976]) ).
cnf(i_0_3676,plain,
~ c_member(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Set_Oimage(X2,X1,c_Nat_OSuc,X3)),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_3673,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924]) ).
cnf(i_0_3677,plain,
c_Fun_Oinj__on(X1,X1,esk7_4(c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4)),X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4)),X1),c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_3673,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144]) ).
cnf(i_0_3678,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1738]) ).
cnf(i_0_3679,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X4))
| c_Fun_Oinj__on(X1,X3,esk7_4(X4,X3,X2,X1),X2)
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1144]) ).
cnf(i_0_3680,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_3673,i_0_2629,i_0_2627,i_0_2195,i_0_2186,i_0_2164,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427]) ).
cnf(i_0_3681,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(rename_variables,[],[i_0_2629]) ).
cnf(i_0_3682,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(rename_variables,[],[i_0_1427]) ).
cnf(i_0_3683,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Set_Oimage(X4,X2,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_3673,i_0_2629,i_0_2627,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423]) ).
cnf(i_0_3684,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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(rename_variables,[],[i_0_2175]) ).
cnf(i_0_3685,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(rename_variables,[],[i_0_1423]) ).
cnf(i_0_3686,plain,
~ c_Orderings_Oord__class_Oless(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426]) ).
cnf(i_0_3687,plain,
c_Orderings_Oord__class_Oless__eq(esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(rename_variables,[],[i_0_2629]) ).
cnf(i_0_3688,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1426]) ).
cnf(i_0_3689,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424]) ).
cnf(i_0_3690,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(rename_variables,[],[i_0_2173]) ).
cnf(i_0_3691,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1424]) ).
cnf(i_0_3692,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425]) ).
cnf(i_0_3693,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,X1)),
inference(rename_variables,[],[i_0_2173]) ).
cnf(i_0_3694,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1425]) ).
cnf(i_0_3695,plain,
~ c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095]) ).
cnf(i_0_3696,plain,
~ c_member(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_2406]) ).
cnf(i_0_3697,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1692]) ).
cnf(i_0_3698,plain,
( c_member(X1,hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5),X6)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X6)
| ~ c_member(X2,X5,c_Set_Oimage(X1,X2,X4,X3))
| ~ c_Fun_Oinj__on(X1,X2,X4,X3) ),
inference(rename_variables,[],[i_0_1095]) ).
cnf(i_0_3699,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Set_Oimage(X4,X2,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428]) ).
cnf(i_0_3700,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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(rename_variables,[],[i_0_2175]) ).
cnf(i_0_3701,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1428]) ).
cnf(i_0_3702,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1)),X2)),X3),X4),X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299]) ).
cnf(i_0_3703,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2),X3),X1),
inference(rename_variables,[],[i_0_2164]) ).
cnf(i_0_3704,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1299]) ).
cnf(i_0_3705,plain,
c_Orderings_Oord__class_Oless__eq(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604]) ).
cnf(i_0_3706,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_1604]) ).
cnf(i_0_3707,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X3),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237]) ).
cnf(i_0_3708,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X4),X3),
inference(rename_variables,[],[i_0_2917]) ).
cnf(i_0_3709,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1237]) ).
cnf(i_0_3710,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276]) ).
cnf(i_0_3711,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X3))),
inference(rename_variables,[],[i_0_2464]) ).
cnf(i_0_3712,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1276]) ).
cnf(i_0_3713,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),X6),c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5))),c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_1738,i_0_2340,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477]) ).
cnf(i_0_3714,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_3715,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),X6),X7) != c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5)),
inference(rename_variables,[],[i_0_3144]) ).
cnf(i_0_3716,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1477]) ).
cnf(i_0_3717,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),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(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274]) ).
cnf(i_0_3718,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1274]) ).
cnf(i_0_3719,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X3)),X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236]) ).
cnf(i_0_3720,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_2150]) ).
cnf(i_0_3721,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1236]) ).
cnf(i_0_3722,plain,
c_Orderings_Oord__class_Oless__eq(c_Nat_Osize__class_Osize(tc_Nat_Onat,esk4_4(hAPP(c_Nat_OSuc,tc_Nat_Onat),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450]) ).
cnf(i_0_3723,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_1450]) ).
cnf(i_0_3724,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4))),X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238]) ).
cnf(i_0_3725,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))),X4),X2),
inference(rename_variables,[],[i_0_3278]) ).
cnf(i_0_3726,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5) ),
inference(rename_variables,[],[i_0_1238]) ).
cnf(i_0_3727,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368]) ).
cnf(i_0_3728,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))),
inference(rename_variables,[],[i_0_2085]) ).
cnf(i_0_3729,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(rename_variables,[],[i_0_1368]) ).
cnf(i_0_3730,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk14_1(c_Set_Oinsert(tc_Nat_Onat,hAPP(X1,X2),c_Set_Oimage(tc_Product__Type_Ounit,tc_Nat_Onat,X1,X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != hAPP(X1,X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522]) ).
cnf(i_0_3731,plain,
( c_member(X1,X2,c_Set_Oinsert(X1,X3,X4))
| X2 != X3 ),
inference(rename_variables,[],[i_0_1522]) ).
cnf(i_0_3732,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,esk4_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat))) != X1,
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832]) ).
cnf(i_0_3733,plain,
~ c_member(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk14_1(c_Set_Oinsert(tc_Nat_Onat,hAPP(X1,X2),c_Set_Oimage(tc_Product__Type_Ounit,tc_Nat_Onat,X1,X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Set_Oimage(tc_Product__Type_Ounit,tc_Nat_Onat,X1,X3)),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395]) ).
cnf(i_0_3734,plain,
( c_member(X1,X2,c_Set_Oinsert(X1,X3,X4))
| ~ c_member(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1395]) ).
cnf(i_0_3735,plain,
hAPP(c_Nat_OSuc,c_Set_Oinsert(tc_Nat_Onat,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) != c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860]) ).
cnf(i_0_3736,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),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(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658]) ).
cnf(i_0_3737,plain,
( ~ 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(rename_variables,[],[i_0_1658]) ).
cnf(i_0_3738,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)))),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533]) ).
cnf(i_0_3739,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1533]) ).
cnf(i_0_3740,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589]) ).
cnf(i_0_3741,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1589]) ).
cnf(i_0_3742,plain,
c_member(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,esk8_4(c_Set_Oinsert(X4,X3,X5),X4,X1,c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,X5))),c_Set_Oinsert(X4,X3,X5))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302]) ).
cnf(i_0_3743,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X3),X4)
| c_member(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1302]) ).
cnf(i_0_3744,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != hAPP(c_Nat_OSuc,X1),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178]) ).
cnf(i_0_3745,plain,
( c_member(X1,X2,c_Set_Oimage(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))
| X2 != hAPP(X4,X5) ),
inference(rename_variables,[],[i_0_1178]) ).
cnf(i_0_3746,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343]) ).
cnf(i_0_3747,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4) ),
inference(rename_variables,[],[i_0_1343]) ).
cnf(i_0_3748,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388]) ).
cnf(i_0_3749,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk27_2(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1388]) ).
cnf(i_0_3750,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460]) ).
cnf(i_0_3751,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(rename_variables,[],[i_0_1460]) ).
cnf(i_0_3752,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1)),esk23_2(hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448]) ).
cnf(i_0_3753,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1448]) ).
cnf(i_0_3754,plain,
hAPP(c_Nat_OSuc,esk4_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)) != X1,
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825]) ).
cnf(i_0_3755,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(X1))) = c_Groups_Ozero__class_Ozero(X1) ),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_3667,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825,i_0_1695]) ).
cnf(i_0_3756,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_1730]) ).
cnf(i_0_3757,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(rename_variables,[],[i_0_1695]) ).
cnf(i_0_3758,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X4)),X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_3667,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825,i_0_1695,i_0_1286]) ).
cnf(i_0_3759,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_1286]) ).
cnf(i_0_3760,plain,
c_member(X1,esk42_2(c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4)),X1),c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(tc_Product__Type_Ounit,X1,X2,X4))),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_3667,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825,i_0_1695,i_0_1286,i_0_1605]) ).
cnf(i_0_3761,plain,
( c_Finite__Set_Ocard(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_member(X1,esk42_2(X2,X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1605]) ).
cnf(i_0_3762,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X4))),X3),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_3667,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825,i_0_1695,i_0_1286,i_0_1605,i_0_1289]) ).
cnf(i_0_3763,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1289]) ).
cnf(i_0_3764,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X3),X2),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_3667,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825,i_0_1695,i_0_1286,i_0_1605,i_0_1289,i_0_1285]) ).
cnf(i_0_3765,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_1285]) ).
cnf(i_0_3766,plain,
( esk23_2(hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk23_2(hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X1))) ),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_3667,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825,i_0_1695,i_0_1286,i_0_1605,i_0_1289,i_0_1285,i_0_1498]) ).
cnf(i_0_3767,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1498]) ).
cnf(i_0_3768,plain,
( c_member(X1,X2,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_3667,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2060,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825,i_0_1695,i_0_1286,i_0_1605,i_0_1289,i_0_1285,i_0_1498,i_0_1247]) ).
cnf(i_0_3769,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X4,X3))
| c_member(X1,X4,X2) ),
inference(rename_variables,[],[i_0_1247]) ).
cnf(i_0_3770,plain,
( ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X3,X2) ),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_3675,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_3667,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2060,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825,i_0_1695,i_0_1286,i_0_1605,i_0_1289,i_0_1285,i_0_1498,i_0_1247,i_0_1326]) ).
cnf(i_0_3771,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X4,X3) ),
inference(rename_variables,[],[i_0_1326]) ).
cnf(i_0_3772,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_3675,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2802,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_3667,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2602,i_0_2276,i_0_2790,i_0_2060,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825,i_0_1695,i_0_1286,i_0_1605,i_0_1289,i_0_1285,i_0_1498,i_0_1247,i_0_1326,i_0_1373]) ).
cnf(i_0_3773,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_1373]) ).
cnf(i_0_3774,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))) ),
inference(scs_inference,[],[i_0_2784,i_0_2834,i_0_2138,i_0_3001,i_0_3245,i_0_3039,i_0_2922,i_0_2448,i_0_3144,i_0_3304,i_0_3249,i_0_3037,i_0_3063,i_0_3092,i_0_2573,i_0_3610,i_0_3612,i_0_3614,i_0_3616,i_0_3618,i_0_3620,i_0_3622,i_0_3624,i_0_3626,i_0_3628,i_0_3630,i_0_3632,i_0_3634,i_0_3636,i_0_3638,i_0_3640,i_0_3642,i_0_3644,i_0_3646,i_0_3648,i_0_3651,i_0_3653,i_0_2150,i_0_3594,i_0_2313,i_0_3479,i_0_3557,i_0_2175,i_0_3684,i_0_3700,i_0_2177,i_0_1976,i_0_3673,i_0_3675,i_0_2629,i_0_3681,i_0_2627,i_0_2173,i_0_3690,i_0_2195,i_0_2186,i_0_2167,i_0_2164,i_0_3483,i_0_2171,i_0_2208,i_0_3657,i_0_3085,i_0_3192,i_0_3184,i_0_3182,i_0_3180,i_0_3178,i_0_3174,i_0_3172,i_0_3170,i_0_3168,i_0_3166,i_0_3162,i_0_3160,i_0_3158,i_0_3156,i_0_3154,i_0_3152,i_0_3150,i_0_2597,i_0_3190,i_0_3148,i_0_3197,i_0_2959,i_0_3357,i_0_3427,i_0_3473,i_0_3487,i_0_2907,i_0_2999,i_0_2983,i_0_3207,i_0_2851,i_0_3351,i_0_3354,i_0_3081,i_0_2181,i_0_3469,i_0_3164,i_0_3195,i_0_3176,i_0_2941,i_0_3205,i_0_3102,i_0_3360,i_0_3398,i_0_3406,i_0_3412,i_0_3201,i_0_3203,i_0_2006,i_0_2707,i_0_2691,i_0_2187,i_0_2098,i_0_3409,i_0_3438,i_0_3450,i_0_2291,i_0_1795,i_0_2337,i_0_1738,i_0_2340,i_0_2802,i_0_2085,i_0_1711,i_0_1543,i_0_2329,i_0_1788,i_0_2809,i_0_2054,i_0_2092,i_0_3390,i_0_2232,i_0_2076,i_0_3373,i_0_3395,i_0_1730,i_0_3341,i_0_3363,i_0_3370,i_0_3379,i_0_3387,i_0_3659,i_0_3661,i_0_3667,i_0_1692,i_0_3476,i_0_3518,i_0_3524,i_0_2464,i_0_2470,i_0_2538,i_0_2602,i_0_2276,i_0_2790,i_0_2060,i_0_2413,i_0_1592,i_0_3554,i_0_2664,i_0_2768,i_0_2548,i_0_3480,i_0_3484,i_0_2483,i_0_1802,i_0_1600,i_0_3531,i_0_1464,i_0_2879,i_0_3323,i_0_2395,i_0_2971,i_0_2900,i_0_3046,i_0_3242,i_0_2892,i_0_3055,i_0_3029,i_0_2869,i_0_3259,i_0_2889,i_0_2917,i_0_3265,i_0_2515,i_0_2968,i_0_3105,i_0_3278,i_0_2933,i_0_3127,i_0_3218,i_0_3227,i_0_3403,i_0_2973,i_0_1803,i_0_1627,i_0_2406,i_0_1591,i_0_1736,i_0_1773,i_0_1776,i_0_1780,i_0_1779,i_0_1783,i_0_1784,i_0_1792,i_0_1171,i_0_1303,i_0_1305,i_0_1687,i_0_1304,i_0_1306,i_0_1828,i_0_1725,i_0_1088,i_0_1114,i_0_1125,i_0_1632,i_0_1633,i_0_1665,i_0_1410,i_0_1588,i_0_1724,i_0_1760,i_0_1332,i_0_1348,i_0_1412,i_0_1506,i_0_1673,i_0_1115,i_0_1333,i_0_1414,i_0_1417,i_0_1507,i_0_1535,i_0_1680,i_0_1170,i_0_1689,i_0_1352,i_0_1537,i_0_1635,i_0_1661,i_0_1664,i_0_1734,i_0_1416,i_0_1429,i_0_1447,i_0_1590,i_0_1674,i_0_1511,i_0_1539,i_0_1691,i_0_1270,i_0_1660,i_0_1351,i_0_1510,i_0_1574,i_0_1581,i_0_1473,i_0_1512,i_0_1444,i_0_1472,i_0_2375,i_0_2376,i_0_1827,i_0_1806,i_0_1377,i_0_1527,i_0_1526,i_0_1645,i_0_1715,i_0_1290,i_0_1124,i_0_1644,i_0_1288,i_0_1284,i_0_1224,i_0_1631,i_0_1651,i_0_1653,i_0_1135,i_0_1451,i_0_1149,i_0_1197,i_0_1693,i_0_1720,i_0_1583,i_0_1400,i_0_1654,i_0_1655,i_0_1382,i_0_1719,i_0_1721,i_0_1541,i_0_1436,i_0_1220,i_0_1174,i_0_1478,i_0_1618,i_0_1702,i_0_1494,i_0_1287,i_0_1486,i_0_1246,i_0_1556,i_0_1283,i_0_1620,i_0_1485,i_0_1245,i_0_1493,i_0_1489,i_0_1558,i_0_1573,i_0_1915,i_0_1807,i_0_1894,i_0_1895,i_0_1896,i_0_1897,i_0_1898,i_0_1900,i_0_1904,i_0_1906,i_0_1908,i_0_1909,i_0_1910,i_0_1911,i_0_1912,i_0_1913,i_0_1914,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1922,i_0_1936,i_0_1937,i_0_1920,i_0_1921,i_0_1923,i_0_1926,i_0_1929,i_0_1930,i_0_1931,i_0_1935,i_0_1925,i_0_1892,i_0_1927,i_0_1928,i_0_1924,i_0_1144,i_0_1427,i_0_1423,i_0_1426,i_0_1424,i_0_1425,i_0_1095,i_0_1428,i_0_1299,i_0_1604,i_0_1237,i_0_1276,i_0_1477,i_0_1274,i_0_1236,i_0_1450,i_0_1238,i_0_1368,i_0_1522,i_0_1832,i_0_1395,i_0_1860,i_0_1658,i_0_1533,i_0_1589,i_0_1302,i_0_1178,i_0_1343,i_0_1388,i_0_1460,i_0_1448,i_0_1825,i_0_1695,i_0_1286,i_0_1605,i_0_1289,i_0_1285,i_0_1498,i_0_1247,i_0_1326,i_0_1373,i_0_1374]) ).
cnf(i_0_3775,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),X3)),
inference(rename_variables,[],[i_0_2538]) ).
cnf(i_0_3776,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_1374]) ).
cnf(i_0_3777,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk12_1(c_Set_Oinsert(tc_Nat_Onat,hAPP(X1,X2),c_Set_Oimage(tc_Product__Type_Ounit,tc_Nat_Onat,X1,X3)))),X4),X5) != hAPP(X1,X2),
inference(scs_inference,[],[i_0_3482,i_0_1522]) ).
cnf(i_0_3778,plain,
( c_member(X1,X2,c_Set_Oinsert(X1,X3,X4))
| X2 != X3 ),
inference(rename_variables,[],[i_0_1522]) ).
cnf(i_0_3779,plain,
~ c_member(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk12_1(c_Set_Oinsert(tc_Nat_Onat,hAPP(X1,X2),c_Set_Oimage(tc_Product__Type_Ounit,tc_Nat_Onat,X1,X3)))),X4),X5),c_Set_Oimage(tc_Product__Type_Ounit,tc_Nat_Onat,X1,X3)),
inference(scs_inference,[],[i_0_3482,i_0_1522,i_0_1395]) ).
cnf(i_0_3780,plain,
( c_member(X1,X2,c_Set_Oinsert(X1,X3,X4))
| ~ c_member(X1,X2,X4) ),
inference(rename_variables,[],[i_0_1395]) ).
cnf(i_0_3781,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_3662,i_0_3482,i_0_1522,i_0_1395,i_0_1533]) ).
cnf(i_0_3782,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_1533]) ).
cnf(i_0_3783,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),
inference(scs_inference,[],[i_0_3665,i_0_3662,i_0_3482,i_0_1522,i_0_1395,i_0_1533,i_0_1589]) ).
cnf(i_0_3784,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_1589]) ).
cnf(i_0_3785,plain,
$false,
inference(scs_inference,[],[i_0_3665,i_0_3662,i_0_1464,i_0_3733,i_0_3482,i_0_1522,i_0_1395,i_0_1533,i_0_1589,i_0_1178]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SCT159+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
% 0.17/0.32 % Computer : n016.cluster.edu
% 0.17/0.32 % Model : x86_64 x86_64
% 0.17/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.32 % Memory : 8042.1875MB
% 0.17/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.32 % CPULimit : 300
% 0.17/0.32 % WCLimit : 300
% 0.17/0.32 % DateTime : Tue May 5 01:59:36 EDT 2026
% 0.17/0.32 % CPUTime :
% 0.17/0.33 % start to proof: theBenchmark
% 5.34/5.73 % Version : CSE_E---1.7
% 5.34/5.73 % Problem : theBenchmark.p
% 5.34/5.73 % SZS status Theorem for theBenchmark.p
% 5.34/5.73 % SZS output start CNFRefutation
% See solution above
% 40.07/34.57 % Total time : 5.395s
%------------------------------------------------------------------------------