%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW232+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.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 05:30:37 PM UTC 2026
% Result : Theorem 1.72s 5.79s
% Output : CNFRefutation 46.36s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1401)
% Comments :
%------------------------------------------------------------------------------
fof(fact_order__2,axiom,
! [X4,X12,X10] :
( class_Rings_Oidom(X10)
=> ( X12 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
=> ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))))),c_Nat_OSuc(c_Polynomial_Oorder(X10,X4,X12))),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__2) ).
fof(fact_order,axiom,
! [X4,X12,X10] :
( class_Rings_Oidom(X10)
=> ( X12 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))))),c_Polynomial_Oorder(X10,X4,X12)),X12)
& ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))))),c_Nat_OSuc(c_Polynomial_Oorder(X10,X4,X12))),X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order) ).
fof(fact_le__SucE,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,c_Nat_OSuc(X33))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> X34 = c_Nat_OSuc(X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_not__less__eq__eq,axiom,
! [X35,X36] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X35),X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X35,X36] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,c_Nat_OSuc(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_less__SucE,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,c_Nat_OSuc(X33))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> X34 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_less__antisym,axiom,
! [X34,X33] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X34)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Nat_OSuc(X34))
=> X34 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X36,X35] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X36)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,c_Nat_OSuc(X36))
<=> X35 = X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X33] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X33),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_Suc__eq__plus1,axiom,
! [X33] : c_Nat_OSuc(X33) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_realpow__two__diff,axiom,
! [X8,X9,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X8),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X9,X8)),c_Groups_Oplus__class_Oplus(X10,X9,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X35))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(fact_reals__Archimedean4,axiom,
! [X9,X8] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> ? [X57] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X57)),X8),X9)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X57))),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean4) ).
fof(fact_lemma__NBseq__def2,axiom,
! [X85,X22] :
( class_RealVector_Oreal__normed__vector(X22)
=> ( ? [X61] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& ! [X57] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X22,hAPP(X85,X57)),X61) )
<=> ? [X86] :
! [X57] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X22,hAPP(X85,X57)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X86))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def2) ).
fof(fact_lemma__NBseq__def,axiom,
! [X85,X22] :
( class_RealVector_Oreal__normed__vector(X22)
=> ( ? [X61] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& ! [X57] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X22,hAPP(X85,X57)),X61) )
<=> ? [X86] :
! [X57] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X22,hAPP(X85,X57)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X86))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def) ).
fof(fact_realpow__two__disj,axiom,
! [X21,X19,X10] :
( class_Rings_Oidom(X10)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X19),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X21),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( X19 = X21
| X19 = c_Groups_Ouminus__class_Ouminus(X10,X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
fof(fact_power__le__imp__le__base,axiom,
! [X13,X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),c_Nat_OSuc(X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),c_Nat_OSuc(X33)))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> c_Orderings_Oord__class_Oless__eq(X10,X4,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_lemma__realpow__diff,axiom,
! [X8,X33,X12,X10] :
( class_Groups_Omonoid__mult(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X33)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X8),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X33),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X8),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X12))),X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__realpow__diff) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [X8,X9,X10] :
( class_Rings_Olinordered__ring(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X8)),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [X35,X17,X81,X82,X10] : hAPP(hAPP(c_Power_Opower_Opower(X10,X82,X81),X17),c_Nat_OSuc(X35)) = hAPP(hAPP(X81,X17),hAPP(hAPP(c_Power_Opower_Opower(X10,X82,X81),X17),X35)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(fact_Suc__mult__cancel1,axiom,
! [X35,X36,X39] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X39)),X35)
<=> X36 = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_one__less__mult,axiom,
! [X34,X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X34)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
fof(fact_one__le__mult__iff,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_diff__Suc__diff__eq2,axiom,
! [X34,X25,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)),X34) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X25),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [X34,X25,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X24),c_Nat_OSuc(X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(fact_power__inject__base,axiom,
! [X13,X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),c_Nat_OSuc(X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),c_Nat_OSuc(X33))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> X4 = X13 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).
fof(fact_int__power__div__base,axiom,
! [X24,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24),X34),X24) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X24),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power__div__base) ).
fof(fact_nat__lt__two__imp__zero__or__one,axiom,
! [X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X9 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
fof(fact_nat__diff__split__asm,axiom,
! [X15,X17,X64] :
( hBOOL(hAPP(X64,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X15)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X15)
& ~ hBOOL(hAPP(X64,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X68] :
( X17 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X68)
& ~ hBOOL(hAPP(X64,X68)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_n__less__n__mult__m,axiom,
! [X34,X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X34)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_n__less__m__mult__n,axiom,
! [X34,X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X34)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_Suc__diff__diff,axiom,
! [X24,X33,X34] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X34),X33),c_Nat_OSuc(X24)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33),X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
fof(fact_power__Suc__less__one,axiom,
! [X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,X4,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),c_Nat_OSuc(X33)),c_Groups_Oone__class_Oone(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_realpow__Suc__le__self,axiom,
! [X33,X29,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X29)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X29,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X29),c_Nat_OSuc(X33)),X29) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
fof(fact_nat__one__le__power,axiom,
! [X33,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
fof(fact_power__gt1,axiom,
! [X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X4)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),c_Nat_OSuc(X33))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
fof(fact_Suc__less__SucD,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X34),c_Nat_OSuc(X33))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__less__eq,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X36),c_Nat_OSuc(X35))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__le__mono,axiom,
! [X36,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X35),c_Nat_OSuc(X36))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_Suc__pred,axiom,
! [X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).
fof(fact_diff__Suc__less,axiom,
! [X26,X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,c_Nat_OSuc(X26)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_ex__least__nat__less,axiom,
! [X35,X64] :
( ~ hBOOL(hAPP(X64,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X64,X35))
=> ? [X37] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X35)
& ! [X69] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X69,X37)
=> ~ hBOOL(hAPP(X64,X69)) )
& hBOOL(hAPP(X64,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_add__eq__if,axiom,
! [X33,X34] :
( ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33) = X33 )
& ( X34 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
! [X11,X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X11)),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),c_Nat_OSuc(X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(fact_power__Suc2,axiom,
! [X33,X4,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),c_Nat_OSuc(X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
fof(fact_mult__Suc,axiom,
! [X33,X34] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X34)),X33) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
fof(fact_Suc__diff__le,axiom,
! [X34,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X34)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X34),X33) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
fof(fact_less__add__Suc1,axiom,
! [X34,X26] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X34))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X34,X26] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X26))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_le__Suc__eq,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,c_Nat_OSuc(X35))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35)
| X36 = c_Nat_OSuc(X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_dvd_Oless__trans,axiom,
! [X14,X8,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X9) )
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X8) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
fof(fact_Suc__mono,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X34),c_Nat_OSuc(X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Nat_OSuc(X35))
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X75] :
( X36 = c_Nat_OSuc(X75)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X75,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_le__less__Suc__eq,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,c_Nat_OSuc(X36))
<=> X35 = X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_monom__Suc,axiom,
! [X33,X4,X10] :
( class_Groups_Ozero(X10)
=> c_Polynomial_Omonom(X10,X4,c_Nat_OSuc(X33)) = c_Polynomial_OpCons(X10,c_Groups_Ozero__class_Ozero(X10),c_Polynomial_Omonom(X10,X4,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__Suc) ).
fof(fact_power__Suc__0,axiom,
! [X33] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
fof(fact_less__trans__Suc,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X26),X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_dvd__1__iff__1,axiom,
! [X36] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
fof(fact_diff__Suc__Suc,axiom,
! [X33,X34] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X34),c_Nat_OSuc(X33)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
fof(fact_add__Suc__shift,axiom,
! [X33,X34] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X34),X33) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,c_Nat_OSuc(X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_diff__Suc__eq__diff__pred,axiom,
! [X33,X34] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Nat_OSuc(X33)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
fof(fact_power__Suc,axiom,
! [X33,X4,X10] :
( class_Power_Opower(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),c_Nat_OSuc(X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
! [X11,X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),c_Nat_OSuc(X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
! [X11,X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X11)) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),c_Nat_OSuc(X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(fact_add__Suc,axiom,
! [X33,X34] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X34),X33) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__right,axiom,
! [X33,X34] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,c_Nat_OSuc(X33)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_less__Suc__eq,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Nat_OSuc(X35))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35)
| X36 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__lessD,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X34),X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__le__lessD,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X34),X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_Suc__le__eq,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X36),X35)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_less__eq__Suc__le,axiom,
! [X36,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X36)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X35),X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__leD,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X34),X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_less__Suc__eq__le,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Nat_OSuc(X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_less__iff__Suc__add,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35)
<=> ? [X37] : X35 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_dvd_Ole__less__trans,axiom,
! [X14,X8,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X8) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
fof(fact_dvd_Oless__le__trans,axiom,
! [X14,X8,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X9) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X14)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
fof(fact_Suc__lessI,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> ( c_Nat_OSuc(X34) != X33
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X34),X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_add__leE,axiom,
! [X33,X24,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X24),X33)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_mult__Suc__right,axiom,
! [X33,X34] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),c_Nat_OSuc(X33)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_real__of__nat__Suc__gt__zero,axiom,
! [X33] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X33))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
fof(fact_one__is__add,axiom,
! [X35,X36] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X35)
<=> ( ( X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X35 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(fact_add__is__1,axiom,
! [X35,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X35) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X35 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X10,X22] :
( class_Orderings_Oord(X22)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X10,X22),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_mult__eq__1__iff,axiom,
! [X35,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X36 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X35 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
fof(fact_less__Suc0,axiom,
! [X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_diff__less__Suc,axiom,
! [X33,X34] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33),c_Nat_OSuc(X34)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_not__square__less__zero,axiom,
! [X4,X10] :
( class_Rings_Olinordered__ring(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X4),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_zdvd__not__zless,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X34)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X34,X33)
=> ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X33,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
fof(fact_nat__dvd__not__less,axiom,
! [X33,X34] :
( 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,X34,X33)
=> ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X33,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
fof(fact_Suc__diff__1,axiom,
! [X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
fof(fact_Suc__pred_H,axiom,
! [X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> X33 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
fof(fact_Suc__leI,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X34),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_less__SucI,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,c_Nat_OSuc(X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_le__imp__less__Suc,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,c_Nat_OSuc(X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_le__SucI,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,c_Nat_OSuc(X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_not__add__less1,axiom,
! [X25,X26] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X25),X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X26,X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X26),X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_not__real__square__gt__zero,axiom,
! [X19] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X19),X19))
<=> X19 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [X36,X19] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X36) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_add__diff__inverse,axiom,
! [X33,X34] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33)) = X34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_less__le__not__le,axiom,
! [X21,X19,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
& ~ c_Orderings_Oord__class_Oless__eq(X10,X21,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_real__of__nat__Suc,axiom,
! [X33] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X33)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X33),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
fof(fact_power__0__Suc,axiom,
! [X33,X10] :
( ( class_Power_Opower(X10)
& class_Rings_Osemiring__0(X10) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ozero__class_Ozero(X10)),c_Nat_OSuc(X33)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> X19 = X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X4,X13,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X13,X4)
=> ~ c_Orderings_Oord__class_Oless(X10,X4,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> ( c_Orderings_Oord__class_Oless(X10,X21,X19)
| X19 = X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_linorder__not__less,axiom,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> c_Orderings_Oord__class_Oless__eq(X10,X21,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_leD,axiom,
! [X9,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X9)
=> ~ c_Orderings_Oord__class_Oless(X10,X9,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__le,axiom,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
<=> c_Orderings_Oord__class_Oless(X10,X21,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_order__less__not__sym,axiom,
! [X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_order__less__imp__not__less,axiom,
! [X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__asym_H,axiom,
! [X13,X4,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ~ c_Orderings_Oord__class_Oless(X10,X13,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__asym,axiom,
! [X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_Suc__inject,axiom,
! [X8,X9] :
( c_Nat_OSuc(X9) = c_Nat_OSuc(X8)
=> X9 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(fact_nat_Oinject,axiom,
! [X70,X71] :
( c_Nat_OSuc(X71) = c_Nat_OSuc(X70)
<=> X71 = X70 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_dvd_Ole__neq__trans,axiom,
! [X13,X4] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13)
=> ( X4 != X13
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
fof(fact_dvd_Ole__imp__less__or__eq,axiom,
! [X8,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X9) )
| X9 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
fof(fact_dvd_Oneq__le__trans,axiom,
! [X13,X4] :
( X4 != X13
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
fof(fact_dvd_Oless__le,axiom,
! [X21,X19] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X21)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X19) )
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X21)
& X19 != X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
fof(fact_dvd_Ole__less,axiom,
! [X21,X19] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X21)
<=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X21)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X19) )
| X19 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
fof(fact_dvd__1__left,axiom,
! [X24] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).
fof(fact_diff__Suc__1,axiom,
! [X33] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X33),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
fof(fact_zero__less__Suc,axiom,
! [X33] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_lessI,axiom,
! [X33] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Nat_OSuc(X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_gr0__conv__Suc,axiom,
! [X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X35)
<=> ? [X74] : X35 = c_Nat_OSuc(X74) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_tsub__def,axiom,
! [X9,X8] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X9)
=> c_Nat__Transfer_Otsub(X9,X8) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X8) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X9)
=> c_Nat__Transfer_Otsub(X9,X8) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__def) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X19,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
<=> X19 = X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_norm__not__less__zero,axiom,
! [X9,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
fof(fact_not__real__of__nat__less__zero,axiom,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X33),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X8,X9,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( X9 != X8
=> ( ~ c_Orderings_Oord__class_Oless(X10,X9,X8)
=> c_Orderings_Oord__class_Oless(X10,X8,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X19,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X21,X19)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> X19 = X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE,axiom,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( X9 != X8
=> ( ~ c_Orderings_Oord__class_Oless(X10,X9,X8)
=> c_Orderings_Oord__class_Oless(X10,X8,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__cases,axiom,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X9,X8)
=> ( X9 != X8
=> c_Orderings_Oord__class_Oless(X10,X8,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_not__leE,axiom,
! [X9,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X8,X9)
=> c_Orderings_Oord__class_Oless(X10,X9,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_linorder__le__cases,axiom,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_not__one__less__zero,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_not__one__le__zero,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X33] : c_Nat_OSuc(X33) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_linorder__neqE__nat,axiom,
! [X8,X9] :
( X9 != X8
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X8)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_order__less__irrefl,axiom,
! [X9,X10] :
( class_Orderings_Opreorder(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,X9,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_Suc__neq__Zero,axiom,
! [X34] : c_Nat_OSuc(X34) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [X73] : c_Nat_OSuc(X73) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__not__Zero,axiom,
! [X34] : c_Nat_OSuc(X34) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_Zero__neq__Suc,axiom,
! [X34] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X72] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X72),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__not__Suc,axiom,
! [X34] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_Suc__n__not__n,axiom,
! [X33] : c_Nat_OSuc(X33) != X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X33] : X33 != c_Nat_OSuc(X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_not__less0,axiom,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__nat__zero__code,axiom,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_less__zeroE,axiom,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__not__refl,axiom,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_less__irrefl__nat,axiom,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_not__pos__poly__0,axiom,
! [X10] :
( class_Rings_Olinordered__idom(X10)
=> ~ c_Polynomial_Opos__poly(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
fof(help_c__fequal__1,axiom,
! [X21,X19] :
( ~ hBOOL(c_fequal(X19,X21))
| X19 = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_lemmaCauchy,axiom,
! [X85,X87,X10,X22] :
( ( class_RealVector_Oreal__normed__vector(X22)
& class_Orderings_Oord(X10) )
=> ( ! [X57] :
( c_Orderings_Oord__class_Oless__eq(X10,X87,X57)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X22,c_Groups_Ominus__class_Ominus(X22,hAPP(X85,X87),hAPP(X85,X57))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
=> ! [X57] :
( c_Orderings_Oord__class_Oless__eq(X10,X87,X57)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X22,hAPP(X85,X57)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X22,hAPP(X85,X87)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemmaCauchy) ).
fof(fact_poly__rec_Osimps,axiom,
! [X20,X17,X2,X28,X10,X22] :
( class_Groups_Ozero(X22)
=> c_Polynomial_Opoly__rec(X10,X22,X28,X2,c_Polynomial_OpCons(X22,X17,X20)) = hAPP(hAPP(hAPP(X2,X17),X20),c_If(X10,c_fequal(X20,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X22))),X28,c_Polynomial_Opoly__rec(X10,X22,X28,X2,X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec_Osimps) ).
fof(fact_poly__rec__pCons,axiom,
! [X20,X17,X10,X28,X2,X22] :
( class_Groups_Ozero(X22)
=> ( hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X22)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X22))),X28) = X28
=> c_Polynomial_Opoly__rec(X10,X22,X28,X2,c_Polynomial_OpCons(X22,X17,X20)) = hAPP(hAPP(hAPP(X2,X17),X20),c_Polynomial_Opoly__rec(X10,X22,X28,X2,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__pCons) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X10,X22] :
( class_Orderings_Oord(X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X22,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [X13,X4,X8,X9,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X9,X4)),c_Groups_Ominus__class_Ominus(X10,X8,X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X9,X4)),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Ominus__class_Ominus(X10,X8,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_synthetic__div__correct_H,axiom,
! [X12,X18,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X18),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))))),c_Polynomial_Osynthetic__div(X10,X12,X18)),c_Polynomial_OpCons(X10,hAPP(c_Polynomial_Opoly(X10,X12),X18),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)))) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
fof(fact_less__add__iff1,axiom,
! [X46,X15,X16,X54,X17,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X54),X16),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X54),X46))
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X17,X15)),X54),X16),X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(fact_le__add__iff1,axiom,
! [X46,X15,X16,X54,X17,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X54),X16),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X54),X46))
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X17,X15)),X54),X16),X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
fof(fact_less__add__iff2,axiom,
! [X46,X15,X16,X54,X17,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X54),X16),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X54),X46))
<=> c_Orderings_Oord__class_Oless(X10,X16,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X15,X17)),X54),X46)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(fact_le__add__iff2,axiom,
! [X46,X15,X16,X54,X17,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X54),X16),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X54),X46))
<=> c_Orderings_Oord__class_Oless__eq(X10,X16,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X15,X17)),X54),X46)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(fact_nat__less__add__iff1,axiom,
! [X35,X36,X59,X38,X40] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X38)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X59),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X59),X35))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X38,X40)),X59),X36),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_nat__le__add__iff1,axiom,
! [X35,X36,X59,X38,X40] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X59),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X59),X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X38,X40)),X59),X36),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__less__add__iff2,axiom,
! [X35,X36,X59,X40,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X40)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X59),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X59),X35))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X38)),X59),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
fof(fact_nat__le__add__iff2,axiom,
! [X35,X36,X59,X40,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X40)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X59),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X59),X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X38)),X59),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_order__1,axiom,
! [X12,X4,X10] :
( class_Rings_Oidom(X10)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))))),c_Polynomial_Oorder(X10,X4,X12)),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__1) ).
fof(fact_reduce__poly__simple,axiom,
! [X33,X13] :
( X13 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X7] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X13),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X7),X33)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduce__poly__simple) ).
fof(fact_norm__diff__triangle__ineq,axiom,
! [X5,X18,X13,X4,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),c_Groups_Oplus__class_Oplus(X10,X18,X5))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X4,X18)),c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X13,X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).
fof(fact_poly__cont,axiom,
! [X12,X14,X58] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X58)
=> ? [X68] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X68)
& ! [X30] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X30,X14)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X30,X14)),X68) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X12),X30),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X12),X14))),X58) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__cont) ).
fof(fact_nat__diff__add__eq1,axiom,
! [X33,X34,X60,X26,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X26)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X60),X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X60),X33)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X25)),X60),X34),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_nat__diff__add__eq2,axiom,
! [X33,X34,X60,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X60),X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X60),X33)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X26)),X60),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(conj_0,hypothesis,
( ? [X6] :
! [X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),X7))) )
=> v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_inf__period_I4_J,axiom,
! [X83,X84,X46,X10] :
( ( class_Rings_Ocomm__ring(X10)
& class_Rings_Odvd(X10) )
=> ( c_Rings_Odvd__class_Odvd(X10,X46,X84)
=> ! [X3,X37] :
( c_Rings_Odvd__class_Odvd(X10,X46,c_Groups_Oplus__class_Oplus(X10,X3,X83))
<=> c_Rings_Odvd__class_Odvd(X10,X46,c_Groups_Oplus__class_Oplus(X10,c_Groups_Ominus__class_Ominus(X10,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X37),X84)),X83)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
fof(fact_inf__period_I3_J,axiom,
! [X83,X84,X46,X10] :
( ( class_Rings_Ocomm__ring(X10)
& class_Rings_Odvd(X10) )
=> ( c_Rings_Odvd__class_Odvd(X10,X46,X84)
=> ! [X3,X37] :
( c_Rings_Odvd__class_Odvd(X10,X46,c_Groups_Oplus__class_Oplus(X10,X3,X83))
<=> c_Rings_Odvd__class_Odvd(X10,X46,c_Groups_Oplus__class_Oplus(X10,c_Groups_Ominus__class_Ominus(X10,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X37),X84)),X83)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_poly__rec__0,axiom,
! [X10,X28,X2,X22] :
( class_Groups_Ozero(X22)
=> ( hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X22)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X22))),X28) = X28
=> c_Polynomial_Opoly__rec(X10,X22,X28,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X22))) = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__0) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [X79,X80,X50,X29,X11,X13] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X11),X29) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X80),X79)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X80),X79),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,X13)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X80,X11) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [X79,X80,X50,X29,X11,X13] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X11),X29) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X80),X79)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X80),X79))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X50)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X29)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X80) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_zdvd__period,axiom,
! [X16,X83,X19,X46,X17] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,X46)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,X83))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X46)),X83)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__period) ).
fof(fact_mult_Opos__bounded,axiom,
! [X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X61] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& ! [X62,X63] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X62),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X62)),c_RealVector_Onorm__class_Onorm(X10,X63))),X61)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).
fof(fact_mult_Obounded,axiom,
! [X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X61] :
! [X62,X63] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X62),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X62)),c_RealVector_Onorm__class_Onorm(X10,X63))),X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Obounded) ).
fof(fact_mult_Ononneg__bounded,axiom,
! [X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X61] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& ! [X62,X63] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X62),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X62)),c_RealVector_Onorm__class_Onorm(X10,X63))),X61)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ononneg__bounded) ).
fof(fact_unique__quotient__lemma,axiom,
! [X29,X11,X79,X80,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X80),X79),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X11),X29))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X13)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X80,X11) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [X29,X11,X79,X80,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X80),X79),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X11),X29))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X29,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,X29)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,X79)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X80) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_nat__eq__add__iff1,axiom,
! [X35,X36,X59,X38,X40] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X38)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X59),X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X59),X35)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X38,X40)),X59),X36) = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__eq__add__iff2,axiom,
! [X35,X36,X59,X40,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X40)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X59),X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X59),X35)
<=> X36 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X38)),X59),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_eq__add__iff1,axiom,
! [X46,X15,X16,X54,X17,X10] :
( class_Rings_Oring(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X54),X16) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X54),X46)
<=> c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X17,X15)),X54),X16) = X46 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [X46,X15,X16,X54,X17,X10] :
( class_Rings_Oring(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X54),X16) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X54),X46)
<=> X16 = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X15,X17)),X54),X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_pCons_Ohyps,axiom,
! [X4,X5] :
( v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
=> ? [X6] :
! [X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X4,v_cs____)),X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons_Ohyps) ).
fof(fact_unimodular__reduce__norm,axiom,
! [X14] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X14,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X14,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unimodular__reduce__norm) ).
fof(fact_mult__diff__mult,axiom,
! [X13,X4,X8,X9,X10] :
( class_Rings_Oring(X10)
=> c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Groups_Ominus__class_Ominus(X10,X8,X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X9,X4)),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
! [X33,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X33)),X9),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
fof(fact_combine__common__factor,axiom,
! [X18,X13,X58,X4,X10] :
( class_Rings_Osemiring(X10)
=> c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X58),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X58),X18)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X4,X13)),X58),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_convex__bound__lt,axiom,
! [X67,X60,X8,X4,X9,X10] :
( class_Rings_Olinordered__semiring__1__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X4)
=> ( c_Orderings_Oord__class_Oless(X10,X8,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X60)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X67)
=> ( c_Groups_Oplus__class_Oplus(X10,X60,X67) = c_Groups_Oone__class_Oone(X10)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X60),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X67),X8)),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_convex__bound__le,axiom,
! [X67,X60,X8,X4,X9,X10] :
( class_Rings_Olinordered__semiring__1(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X60)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X67)
=> ( c_Groups_Oplus__class_Oplus(X10,X60,X67) = c_Groups_Oone__class_Oone(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X60),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X67),X8)),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(fact_unity__coeff__ex,axiom,
! [X56,X64,X10] :
( ( class_Rings_Odvd(X10)
& class_Rings_Osemiring__0(X10) )
=> ( ? [X3] : hBOOL(hAPP(X64,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X56),X3)))
<=> ? [X3] :
( c_Rings_Odvd__class_Odvd(X10,X56,c_Groups_Oplus__class_Oplus(X10,X3,c_Groups_Ozero__class_Ozero(X10)))
& hBOOL(hAPP(X64,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_left__add__mult__distrib,axiom,
! [X24,X25,X60,X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X60),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X60),X24)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X25)),X60),X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X21,X19,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X19),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X21),X21)))
<=> ( X19 != c_Groups_Ozero__class_Ozero(X10)
| X21 != c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X42,X43,X44,X45,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X43),X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),X44)),X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X21,X19,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X19),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X21),X21)),c_Groups_Ozero__class_Ozero(X10))
<=> ( X19 = c_Groups_Ozero__class_Ozero(X10)
& X21 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_mult__pCons__left,axiom,
! [X11,X12,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,X4,X12)),X11) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X4,X11),c_Polynomial_OpCons(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X12),X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
fof(fact_poly__eq__0__iff__dvd,axiom,
! [X16,X20,X10] :
( class_Rings_Oidom(X10)
=> ( hAPP(c_Polynomial_Opoly(X10,X20),X16) = c_Groups_Ozero__class_Ozero(X10)
<=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X16),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)))),X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
fof(fact_offset__poly__pCons,axiom,
! [X31,X12,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,c_Polynomial_OpCons(X10,X4,X12),X31) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X31,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X12,X31)),c_Polynomial_OpCons(X10,X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X12,X31))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(fact_realpow__minus__mult,axiom,
! [X9,X33,X10] :
( class_Groups_Omonoid__mult(X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
fof(fact_dvd__iff__poly__eq__0,axiom,
! [X20,X16,X10] :
( class_Rings_Oidom(X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),c_Polynomial_OpCons(X10,X16,c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)))),X20)
<=> hAPP(c_Polynomial_Opoly(X10,X20),c_Groups_Ouminus__class_Ouminus(X10,X16)) = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
fof(fact_crossproduct__noteq,axiom,
! [X46,X16,X15,X17,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( ( X17 != X15
& X16 != X46 )
<=> c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X46)) != c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X46),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X28,X19,X21,X51,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X51),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X19),X28)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X51),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X19),X21))
<=> ( X51 = X19
| X21 = X28 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_div__mult__div__if__dvd,axiom,
! [X23,X14,X9,X8,X10] :
( class_Divides_Osemiring__div(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X8,X9)
=> ( c_Rings_Odvd__class_Odvd(X10,X14,X23)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Divides_Odiv__class_Odiv(X10,X9,X8)),c_Divides_Odiv__class_Odiv(X10,X23,X14)) = c_Divides_Odiv__class_Odiv(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__div__if__dvd) ).
fof(fact_mult__pCons__right,axiom,
! [X11,X4,X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X12),c_Polynomial_OpCons(X10,X4,X11)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X4,X12),c_Polynomial_OpCons(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X12),X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
fof(fact_power__minus,axiom,
! [X33,X4,X10] :
( class_Rings_Oring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ouminus__class_Ouminus(X10,X4)),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10))),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
fof(fact_q__neg__lemma,axiom,
! [X79,X80,X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X80),X79),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X80,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_q__pos__lemma,axiom,
! [X79,X80,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X50),X80),X79))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X50)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X80) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_pcompose__pCons,axiom,
! [X11,X12,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Opcompose(X10,c_Polynomial_OpCons(X10,X4,X12),X11) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_OpCons(X10,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X11),c_Polynomial_Opcompose(X10,X12,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X42,X43,X44,X45,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X43),X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),X43)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X44),X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X42,X43,X44,X45,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X43),X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X43),X42))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_complex__mod__triangle__ineq2,axiom,
! [X4,X13] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X13,X4)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X13)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [X14,X23] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X23),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X23,X14)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(fact_mult__poly__add__left,axiom,
! [X29,X11,X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X12,X11)),X29) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X12),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X11),X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
fof(fact_nat__diff__split,axiom,
! [X15,X17,X64] :
( hBOOL(hAPP(X64,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X15)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X15)
=> hBOOL(hAPP(X64,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X68] :
( X17 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X68)
=> hBOOL(hAPP(X64,X68)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(fact_mult__monom,axiom,
! [X33,X13,X34,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Polynomial_Omonom(X10,X4,X34)),c_Polynomial_Omonom(X10,X13,X33)) = c_Polynomial_Omonom(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__monom) ).
fof(fact_power__Suc__less,axiom,
! [X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,X4,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_div__dvd__div,axiom,
! [X16,X15,X17,X10] :
( class_Divides_Osemiring__div(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X17,X15)
=> ( c_Rings_Odvd__class_Odvd(X10,X17,X16)
=> ( c_Rings_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Odiv(X10,X15,X17),c_Divides_Odiv__class_Odiv(X10,X16,X17))
<=> c_Rings_Odvd__class_Odvd(X10,X15,X16) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__dvd__div) ).
fof(fact_odd__less__0,axiom,
! [X28] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X28),X28),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(fact_norm__add__less,axiom,
! [X66,X8,X29,X9,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X9),X29)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X8),X66)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Groups_Oplus__class_Oplus(X10,X9,X8)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X29,X66)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__add__less) ).
fof(fact_poly__mult,axiom,
! [X9,X11,X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X12),X11)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Polynomial_Opoly(X10,X12),X9)),hAPP(c_Polynomial_Opoly(X10,X11),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(fact_mult__eq__if,axiom,
! [X33,X34] :
( ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X34 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(fact_less__diff__iff,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X35)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X39),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X39))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(fact_le__diff__iff,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X35)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X39),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X39))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(fact_mult__strict__mono,axiom,
! [X5,X18,X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless(X10,X18,X5)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_mult__strict__mono_H,axiom,
! [X5,X18,X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless(X10,X18,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__le__less__imp__less,axiom,
! [X5,X18,X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless(X10,X18,X5)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__less__le__imp__less,axiom,
! [X5,X18,X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X18,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__mono_H,axiom,
! [X5,X18,X13,X4,X10] :
( class_Rings_Oordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X18,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__mono,axiom,
! [X5,X18,X13,X4,X10] :
( class_Rings_Oordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X18,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(fact_norm__mult__less,axiom,
! [X66,X8,X29,X9,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X9),X29)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X8),X66)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X29),X66)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).
fof(fact_synthetic__div__correct,axiom,
! [X18,X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X12,c_Polynomial_Osmult(X10,X18,c_Polynomial_Osynthetic__div(X10,X12,X18))) = c_Polynomial_OpCons(X10,hAPP(c_Polynomial_Opoly(X10,X12),X18),c_Polynomial_Osynthetic__div(X10,X12,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
fof(fact_power__mult__distrib,axiom,
! [X33,X13,X4,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X11,X8,X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X8)),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X11)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X8),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_div__power,axiom,
! [X33,X9,X8,X10] :
( class_Divides_Osemiring__div(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X8,X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Divides_Odiv__class_Odiv(X10,X9,X8)),X33) = c_Divides_Odiv__class_Odiv(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X33),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X8),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__power) ).
fof(fact_poly__minimum__modulus__disc,axiom,
! [X12,X29] :
? [X7] :
! [X30] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X30),X29)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X12),X7)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X12),X30))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minimum__modulus__disc) ).
fof(fact_div__add,axiom,
! [X8,X9,X14,X10] :
( class_Divides_Osemiring__div(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X14,X9)
=> ( c_Rings_Odvd__class_Odvd(X10,X14,X8)
=> c_Divides_Odiv__class_Odiv(X10,c_Groups_Oplus__class_Oplus(X10,X9,X8),X14) = c_Groups_Oplus__class_Oplus(X10,c_Divides_Odiv__class_Odiv(X10,X9,X14),c_Divides_Odiv__class_Odiv(X10,X8,X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add) ).
fof(fact_sum__squares__ge__zero,axiom,
! [X8,X9,X10] :
( class_Rings_Olinordered__ring(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_zdvd__reduce,axiom,
! [X36,X35,X39] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X39,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X35,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X36)))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X39,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
fof(fact_real__squared__diff__one__factored,axiom,
! [X9,X10] :
( class_Rings_Oring__1(X10)
=> c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X9),c_Groups_Oone__class_Oone(X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oone__class_Oone(X10))),c_Groups_Ominus__class_Ominus(X10,X9,c_Groups_Oone__class_Oone(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(fact_poly__pCons,axiom,
! [X9,X12,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Polynomial_OpCons(X10,X4,X12)),X9) = c_Groups_Oplus__class_Oplus(X10,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),hAPP(c_Polynomial_Opoly(X10,X12),X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(fact_power__less__power__Suc,axiom,
! [X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X4)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_mult__right__less__imp__less,axiom,
! [X13,X18,X4,X10] :
( class_Rings_Olinordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,X4,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [X13,X18,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,X4,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_power__less__imp__less__base,axiom,
! [X13,X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),X33))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> c_Orderings_Oord__class_Oless(X10,X4,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_mult__left__less__imp__less,axiom,
! [X13,X4,X18,X10] :
( class_Rings_Olinordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X13))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,X4,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [X13,X4,X18,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X13))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,X4,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X15,X17,X16,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X16)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X15))
<=> c_Orderings_Oord__class_Oless(X10,X17,X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__right__le__imp__le,axiom,
! [X13,X18,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless__eq(X10,X4,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [X13,X4,X18,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X13))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless__eq(X10,X4,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [X15,X17,X16,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X16)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X15))
<=> c_Orderings_Oord__class_Oless__eq(X10,X17,X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X15,X17,X16,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X16,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X15))
<=> c_Orderings_Oord__class_Oless(X10,X15,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [X15,X17,X16,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X16,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X15))
<=> c_Orderings_Oord__class_Oless__eq(X10,X15,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_power__less__imp__less__exp,axiom,
! [X33,X34,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X34),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X21,X19,X15,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X15)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X15),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X15),X21))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__increasing__iff,axiom,
! [X21,X19,X15,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X15)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X15),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X15),X21))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [X33,X34,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X34),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_diff__pCons,axiom,
! [X11,X13,X12,X4,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),c_Polynomial_OpCons(X10,X4,X12),c_Polynomial_OpCons(X10,X13,X11)) = c_Polynomial_OpCons(X10,c_Groups_Ominus__class_Ominus(X10,X4,X13),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X12,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).
fof(fact_add__pCons,axiom,
! [X11,X13,X12,X4,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_OpCons(X10,X4,X12),c_Polynomial_OpCons(X10,X13,X11)) = c_Polynomial_OpCons(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X12,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).
fof(fact_poly__power,axiom,
! [X9,X33,X12,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(c_Polynomial_Opoly(X10,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X10)),X12),X33)),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Polynomial_Opoly(X10,X12),X9)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).
fof(fact_le__mult__natfloor,axiom,
! [X13,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X4)),c_RComplete_Onatfloor(X13)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X13))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
fof(fact_Deriv_Oadd__diff__add,axiom,
! [X5,X13,X18,X4,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),c_Groups_Oplus__class_Oplus(X10,X13,X5)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Ominus__class_Ominus(X10,X4,X13),c_Groups_Ominus__class_Ominus(X10,X18,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X5,X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),c_Groups_Oplus__class_Oplus(X10,X18,X5)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),c_Groups_Oplus__class_Oplus(X10,X13,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_power__strict__decreasing,axiom,
! [X4,X76,X33,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X76)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,X4,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X76),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_power__decreasing,axiom,
! [X4,X76,X33,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X76)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X76),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(fact_div__mult__self2,axiom,
! [X18,X4,X13,X10] :
( class_Divides_Osemiring__div(X10)
=> ( X13 != c_Groups_Ozero__class_Ozero(X10)
=> c_Divides_Odiv__class_Odiv(X10,c_Groups_Oplus__class_Oplus(X10,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18)),X13) = c_Groups_Oplus__class_Oplus(X10,X18,c_Divides_Odiv__class_Odiv(X10,X4,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2) ).
fof(fact_div__mult__self1,axiom,
! [X18,X4,X13,X10] :
( class_Divides_Osemiring__div(X10)
=> ( X13 != c_Groups_Ozero__class_Ozero(X10)
=> c_Divides_Odiv__class_Odiv(X10,c_Groups_Oplus__class_Oplus(X10,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X13)),X13) = c_Groups_Oplus__class_Oplus(X10,X18,c_Divides_Odiv__class_Odiv(X10,X4,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1) ).
fof(fact_power__strict__mono,axiom,
! [X33,X13,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),X33)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X15,X17,X16,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X15))
<=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X16)
& c_Orderings_Oord__class_Oless(X10,X17,X15) )
| ( c_Orderings_Oord__class_Oless(X10,X16,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless(X10,X15,X17) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X15,X16,X17,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X16))
<=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X16)
& c_Orderings_Oord__class_Oless(X10,X17,X15) )
| ( c_Orderings_Oord__class_Oless(X10,X16,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless(X10,X15,X17) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_mult__left_Opos__bounded,axiom,
! [X8,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X61] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X3),X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X3)),X61)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).
fof(fact_mult__left_Obounded,axiom,
! [X8,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X61] :
! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X3),X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X3)),X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Obounded) ).
fof(fact_mult__left_Ononneg__bounded,axiom,
! [X8,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X61] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X3),X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X3)),X61)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ononneg__bounded) ).
fof(fact_norm__mult__ineq,axiom,
! [X8,X9,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X9)),c_RealVector_Onorm__class_Onorm(X10,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
fof(fact_mult__right_Opos__bounded,axiom,
! [X9,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X61] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X3)),X61)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).
fof(fact_mult__right_Obounded,axiom,
! [X9,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X61] :
! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X3)),X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Obounded) ).
fof(fact_mult__right_Ononneg__bounded,axiom,
! [X9,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X61] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X3)),X61)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ononneg__bounded) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X13,X34,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X34)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X4,X13)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_mult_Odiff__left,axiom,
! [X13,X48,X4,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X4,X48)),X13) = c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X48),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
fof(fact_mult__left_Odiff,axiom,
! [X47,X8,X9,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X9,X8)),X47) = c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X47)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X4,X13)),X18) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_mult_Oadd__left,axiom,
! [X13,X48,X4,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X4,X48)),X13) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X48),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_mult__left_Oadd,axiom,
! [X47,X8,X9,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X9,X8)),X47) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X47)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X4,X13)),X18) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_zdiv__mono2,axiom,
! [X13,X50,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X13),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X50)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
fof(fact_zdiv__mono2__neg,axiom,
! [X13,X50,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X50),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X11,X12,X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X12)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X11)) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X33,X34,X4,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X34)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X43,X44,X45,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),X44)),X43) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),X43)),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_dvd__div__mult,axiom,
! [X18,X13,X4,X10] :
( class_Divides_Osemiring__div(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X4,X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Divides_Odiv__class_Odiv(X10,X13,X4)),X18) = c_Divides_Odiv__class_Odiv(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18),X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__mult) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X5,X18,X13,X4,X29,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( X29 != c_Groups_Ozero__class_Ozero(X10)
=> ( ( X4 = X13
& X18 != X5 )
=> c_Groups_Oplus__class_Oplus(X10,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X29),X18)) != c_Groups_Oplus__class_Oplus(X10,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X29),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_dvd__mult__cancel,axiom,
! [X33,X34,X24] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X33))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X34,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
fof(fact_nat__mult__dvd__cancel1,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(fact_nat__power__less__imp__less,axiom,
! [X33,X34,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X34),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X33))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_real__mult__less__iff1,axiom,
! [X21,X19,X28] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X28)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X19),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X28))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X19,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_mult__le__cancel2,axiom,
! [X35,X39,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X39))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_power__dvd__imp__le,axiom,
! [X33,X34,X26] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X34),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X33))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X26)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).
fof(fact_mult__le__cancel1,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [X21,X19,X28] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X28)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X19),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X28))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [X21,X19,X28] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X28)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X28),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X28),X21))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(fact_natceiling__eq,axiom,
! [X9,X33] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X33),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X33),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(X9) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__eq) ).
fof(fact_norm__triangle__ineq2,axiom,
! [X13,X4,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X4),c_RealVector_Onorm__class_Onorm(X10,X13)),c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X4,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).
fof(fact_norm__diff__ineq,axiom,
! [X13,X4,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X4),c_RealVector_Onorm__class_Onorm(X10,X13)),c_RealVector_Onorm__class_Onorm(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).
fof(fact_norm__triangle__ineq4,axiom,
! [X13,X4,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X4,X13)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X4),c_RealVector_Onorm__class_Onorm(X10,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).
fof(fact_norm__triangle__ineq,axiom,
! [X8,X9,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Groups_Oplus__class_Oplus(X10,X9,X8)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X9),c_RealVector_Onorm__class_Onorm(X10,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
fof(fact_mult__smult__left,axiom,
! [X11,X12,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Polynomial_Osmult(X10,X4,X12)),X11) = c_Polynomial_Osmult(X10,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X12),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__left) ).
fof(fact_poly__diff,axiom,
! [X9,X11,X12,X10] :
( class_Rings_Ocomm__ring(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X12,X11)),X9) = c_Groups_Ominus__class_Ominus(X10,hAPP(c_Polynomial_Opoly(X10,X12),X9),hAPP(c_Polynomial_Opoly(X10,X11),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).
fof(fact_poly__add,axiom,
! [X9,X11,X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X12,X11)),X9) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Polynomial_Opoly(X10,X12),X9),hAPP(c_Polynomial_Opoly(X10,X11),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).
fof(fact_power__le__dvd,axiom,
! [X34,X13,X33,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33),X13)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X34),X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__dvd) ).
fof(fact_le__diff__conv2,axiom,
! [X38,X40,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X40)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X39))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X39),X40) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [X23,X52,X53] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X53,X52)),X23) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X52),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X23,X52,X53] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X53,X52)),X23) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X52),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_diff__mult__distrib,axiom,
! [X24,X33,X34] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33)),X24) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X24,X33,X34] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33)),X24) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_real__add__mult__distrib,axiom,
! [X23,X52,X53] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X53,X52)),X23) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X53),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X52),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_norm__power__ineq,axiom,
! [X33,X9,X10] :
( class_RealVector_Oreal__normed__algebra__1(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X9)),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
fof(fact_add__less__cancel__right,axiom,
! [X15,X16,X17,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X17,X16),c_Groups_Oplus__class_Oplus(X10,X15,X16))
<=> c_Orderings_Oord__class_Oless(X10,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__right,axiom,
! [X13,X18,X4,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),c_Groups_Oplus__class_Oplus(X10,X13,X18))
=> c_Orderings_Oord__class_Oless(X10,X4,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__left,axiom,
! [X15,X17,X16,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X16,X17),c_Groups_Oplus__class_Oplus(X10,X16,X15))
<=> c_Orderings_Oord__class_Oless(X10,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__imp__less__left,axiom,
! [X13,X4,X18,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X18,X4),c_Groups_Oplus__class_Oplus(X10,X18,X13))
=> c_Orderings_Oord__class_Oless(X10,X4,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__le__imp__le__right,axiom,
! [X13,X18,X4,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),c_Groups_Oplus__class_Oplus(X10,X13,X18))
=> c_Orderings_Oord__class_Oless__eq(X10,X4,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__right,axiom,
! [X15,X16,X17,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X17,X16),c_Groups_Oplus__class_Oplus(X10,X15,X16))
<=> c_Orderings_Oord__class_Oless__eq(X10,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [X13,X4,X18,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X18,X4),c_Groups_Oplus__class_Oplus(X10,X18,X13))
=> c_Orderings_Oord__class_Oless__eq(X10,X4,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__cancel__left,axiom,
! [X15,X17,X16,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X16,X17),c_Groups_Oplus__class_Oplus(X10,X16,X15))
<=> c_Orderings_Oord__class_Oless__eq(X10,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [X33,X34,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X33)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X24),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X24)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [X15,X17,X16,X10] :
( class_Rings_Oidom(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X15))
<=> ( X16 = c_Groups_Ozero__class_Ozero(X10)
| c_Rings_Odvd__class_Odvd(X10,X17,X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [X15,X16,X17,X10] :
( class_Rings_Oidom(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X16))
<=> ( X16 = c_Groups_Ozero__class_Ozero(X10)
| c_Rings_Odvd__class_Odvd(X10,X17,X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_power__gt1__lemma,axiom,
! [X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X4)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_dvd__diffD,axiom,
! [X33,X34,X24] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33))
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X34)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X34) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD) ).
fof(fact_dvd__diffD1,axiom,
! [X33,X34,X24] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33))
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X34)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X33) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
fof(fact_dvd__div__div__eq__mult,axiom,
! [X46,X15,X16,X17,X10] :
( class_Divides_Osemiring__div(X10)
=> ( X17 != c_Groups_Ozero__class_Ozero(X10)
=> ( X16 != c_Groups_Ozero__class_Ozero(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X17,X15)
=> ( c_Rings_Odvd__class_Odvd(X10,X16,X46)
=> ( c_Divides_Odiv__class_Odiv(X10,X15,X17) = c_Divides_Odiv__class_Odiv(X10,X46,X16)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X46) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__div__eq__mult) ).
fof(fact_zpower__zadd__distrib,axiom,
! [X14,X8,X9] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X14)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X8)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_offset__poly__eq__0__lemma,axiom,
! [X4,X12,X18,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X18,X12),c_Polynomial_OpCons(X10,X4,X12)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
=> X12 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X35))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X35))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_self__quotient__aux2,axiom,
! [X11,X29,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( X4 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X11))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X29)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_self__quotient__aux1,axiom,
! [X11,X29,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( X4 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X11))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_smult__diff__right,axiom,
! [X11,X12,X4,X10] :
( class_Rings_Ocomm__ring(X10)
=> c_Polynomial_Osmult(X10,X4,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X12,X11)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X4,X12),c_Polynomial_Osmult(X10,X4,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__right) ).
fof(fact_smult__add__right,axiom,
! [X11,X12,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,X4,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X12,X11)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X4,X12),c_Polynomial_Osmult(X10,X4,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__right) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [X13,X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),X33)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> X4 = X13 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X34,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X34),X34) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Oone__class_Oone(X10))),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X4,X34,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X34,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X34)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Oone__class_Oone(X10))),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_natfloor__eq,axiom,
! [X9,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X33),X9)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X9,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X33),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatfloor(X9) = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__eq) ).
fof(fact_mult__right__le__one__le,axiom,
! [X8,X9,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X8)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X8),X9) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,axiom,
! [X8,X9,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X8)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X9),X9) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_norm__ratiotest__lemma,axiom,
! [X8,X9,X18,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),c_RealVector_Onorm__class_Onorm(X10,X8)))
=> X9 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
fof(fact_mult__strict__right__mono,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Olinordered__comm__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_power__mono,axiom,
! [X33,X13,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
fof(fact_mult__right__mono,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Oordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(fact_comm__mult__left__mono,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Oordered__comm__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Oordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X18,X4,X13,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X13,X4)
=> ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X18,X4,X13,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X13,X4)
=> ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [X18,X4,X13,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X18,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_mult__left__mono__neg,axiom,
! [X18,X4,X13,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X18,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_le__add__diff,axiom,
! [X34,X33,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34),X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(fact_add__strict__mono,axiom,
! [X5,X18,X13,X4,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless(X10,X18,X5)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),c_Groups_Oplus__class_Oplus(X10,X13,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X5,X18,X13,X4,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless(X10,X18,X5)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),c_Groups_Oplus__class_Oplus(X10,X13,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X5,X18,X13,X4,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X18,X5)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),c_Groups_Oplus__class_Oplus(X10,X13,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__mono,axiom,
! [X5,X18,X13,X4,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X18,X5)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),c_Groups_Oplus__class_Oplus(X10,X13,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_power__strict__increasing,axiom,
! [X4,X76,X33,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X76)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X4)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X76)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__increasing,axiom,
! [X4,X76,X33,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X76)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),X4)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X76)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(fact_diff__monom,axiom,
! [X13,X33,X4,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),c_Polynomial_Omonom(X10,X4,X33),c_Polynomial_Omonom(X10,X13,X33)) = c_Polynomial_Omonom(X10,c_Groups_Ominus__class_Ominus(X10,X4,X13),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__monom) ).
fof(fact_add__monom,axiom,
! [X13,X33,X4,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Omonom(X10,X4,X33),c_Polynomial_Omonom(X10,X13,X33)) = c_Polynomial_Omonom(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__monom) ).
fof(fact_smult__diff__left,axiom,
! [X12,X13,X4,X10] :
( class_Rings_Ocomm__ring(X10)
=> c_Polynomial_Osmult(X10,c_Groups_Ominus__class_Ominus(X10,X4,X13),X12) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X4,X12),c_Polynomial_Osmult(X10,X13,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__left) ).
fof(fact_smult__add__left,axiom,
! [X12,X13,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),X12) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X4,X12),c_Polynomial_Osmult(X10,X13,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__left) ).
fof(fact_mult__dvd__mono,axiom,
! [X5,X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X4,X13)
=> ( c_Rings_Odvd__class_Odvd(X10,X18,X5)
=> c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
fof(fact_realpow__num__eq__if,axiom,
! [X34,X33,X10] :
( class_Power_Opower(X10)
=> ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X34),X33) = c_Groups_Oone__class_Oone(X10) )
& ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X34),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X34),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(fact_dvd__power__le,axiom,
! [X34,X33,X8,X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X9,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X34)
=> c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X33),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X8),X34)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__le) ).
fof(fact_zdiv__mono1,axiom,
! [X13,X48,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X48)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X13),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X48,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
fof(fact_zdiv__mono1__neg,axiom,
! [X13,X48,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X48)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X48,X13),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
fof(fact_smult__pCons,axiom,
! [X12,X13,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,X4,c_Polynomial_OpCons(X10,X13,X12)) = c_Polynomial_OpCons(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),c_Polynomial_Osmult(X10,X4,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
fof(fact_zadd__zless__mono,axiom,
! [X14,X77,X23,X78] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X77,X14)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X78,X77),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_diff__less__mono,axiom,
! [X18,X13,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X4)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X18),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X13,X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(fact_diff__less__mono2,axiom,
! [X41,X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X41)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,X33),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_add__less__mono,axiom,
! [X41,X24,X25,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X41)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X24),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X41)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_add__le__mono,axiom,
! [X41,X24,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X24),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X41)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X21,X19,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X19),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X21),X21)) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X19 = c_Groups_Ozero__class_Ozero(X10)
& X21 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_mult_Odiff__right,axiom,
! [X50,X13,X4,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Ominus__class_Ominus(X10,X13,X50)) = c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X50)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
fof(fact_mult__right_Odiff,axiom,
! [X8,X9,X49,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X49),c_Groups_Ominus__class_Ominus(X10,X9,X8)) = c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X49),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X49),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
fof(fact_mult_Oadd__right,axiom,
! [X50,X13,X4,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Oplus__class_Oplus(X10,X13,X50)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X50)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_mult__right_Oadd,axiom,
! [X8,X9,X49,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X49),c_Groups_Oplus__class_Oplus(X10,X9,X8)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X49),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X49),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X14,X8,X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Groups_Oplus__class_Oplus(X10,X8,X14)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_zdvd__mono,axiom,
! [X83,X36,X39] :
( X39 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X36,X83)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X83)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).
fof(fact_zdvd__mult__cancel,axiom,
! [X33,X34,X24] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X33))
=> ( X24 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X34,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
fof(fact_nat__mult__dvd__cancel__disj,axiom,
! [X35,X36,X39] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35))
<=> ( X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(fact_pow__divides__eq__int,axiom,
! [X15,X17,X35] :
( X35 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17),X35),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15),X35))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).
fof(fact_pow__divides__pow__int,axiom,
! [X13,X33,X4] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4),X33),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13),X33))
=> ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__int) ).
fof(fact_pow__divides__pow__nat,axiom,
! [X13,X33,X4] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4),X33),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13),X33))
=> ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__nat) ).
fof(fact_pow__divides__eq__nat,axiom,
! [X15,X17,X35] :
( X35 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X35),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X35))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).
fof(fact_mult__less__cancel1,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X35,X39,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X39))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
! [X15,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X17,X15))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X17)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X4,X13,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X4))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_power__commutes,axiom,
! [X33,X4,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X43,X44,X45,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),X44)),X43) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X44),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X42,X43,X45,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X43),X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),X43)),X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_nat__less__real__le,axiom,
! [X36,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X36)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X35),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_nat__le__real__less,axiom,
! [X36,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X36)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X35),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X36),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
fof(fact_poly__monom,axiom,
! [X9,X33,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Polynomial_Omonom(X10,X4,X33)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(fact_synthetic__div__unique,axiom,
! [X29,X11,X18,X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X12,c_Polynomial_Osmult(X10,X18,X11)) = c_Polynomial_OpCons(X10,X29,X11)
=> ( X29 = hAPP(c_Polynomial_Opoly(X10,X12),X18)
& X11 = c_Polynomial_Osynthetic__div(X10,X12,X18) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
fof(fact_div__mult__swap,axiom,
! [X4,X13,X18,X10] :
( class_Divides_Osemiring__div(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X18,X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Divides_Odiv__class_Odiv(X10,X13,X18)) = c_Divides_Odiv__class_Odiv(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__swap) ).
fof(fact_reals__Archimedean6,axiom,
! [X29] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X29)
=> ? [X57] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X57,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X29,c_RealDef_Oreal(tc_Nat_Onat,X57)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6) ).
fof(fact_synthetic__div__pCons,axiom,
! [X18,X12,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osynthetic__div(X10,c_Polynomial_OpCons(X10,X4,X12),X18) = c_Polynomial_OpCons(X10,hAPP(c_Polynomial_Opoly(X10,X12),X18),c_Polynomial_Osynthetic__div(X10,X12,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
fof(fact_poly__offset__poly,axiom,
! [X9,X31,X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X12,X31)),X9) = hAPP(c_Polynomial_Opoly(X10,X12),c_Groups_Oplus__class_Oplus(X10,X31,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
fof(fact_power__mult,axiom,
! [X33,X34,X4,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X34)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X11,X12,X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X12)),X11) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_zmult__zless__mono2,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X26,X25)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_real__mult__less__mono2,axiom,
! [X8,X9,X14] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X9,X8)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_power__eq__if,axiom,
! [X12,X34] :
( ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X34) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X34 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X34) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(fact_less__diff__conv,axiom,
! [X39,X40,X38] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X39))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X39),X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(fact_le__diff__conv,axiom,
! [X38,X39,X40] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X39),X38)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_mult__le__mono,axiom,
! [X41,X24,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X41)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(fact_diff__add__assoc2,axiom,
! [X26,X25,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X26),X24) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_add__diff__assoc2,axiom,
! [X26,X25,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24),X26) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X26),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc,axiom,
! [X26,X25,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X25),X24) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_diff__diff__right,axiom,
! [X26,X25,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X24),X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(fact_add__diff__assoc,axiom,
! [X26,X25,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X25),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [X17,X15] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X17,X15))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
! [X17,X15] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X17,X15))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
fof(fact_mult__smult__right,axiom,
! [X11,X4,X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X12),c_Polynomial_Osmult(X10,X4,X11)) = c_Polynomial_Osmult(X10,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X12),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__right) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [X38,X39] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X38,X39))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X38) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_poly__smult,axiom,
! [X9,X12,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Polynomial_Osmult(X10,X4,X12)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),hAPP(c_Polynomial_Opoly(X10,X12),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(fact_mult__le__0__iff,axiom,
! [X15,X17,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X15),c_Groups_Ozero__class_Ozero(X10))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17)
& c_Orderings_Oord__class_Oless__eq(X10,X15,c_Groups_Ozero__class_Ozero(X10)) )
| ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X15) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [X15,X17,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X15))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17)
& c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X15) )
| ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless__eq(X10,X15,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zdvd__zdiffD,axiom,
! [X33,X34,X24] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X24,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X34,X33))
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X24,X33)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X24,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [X52,X53,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X53,X52)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X52)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X52,X53,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X53,X52)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X52)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_diff__mult__distrib2,axiom,
! [X33,X34,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X33,X34,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_poly__pcompose,axiom,
! [X9,X11,X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Polynomial_Opcompose(X10,X12,X11)),X9) = hAPP(c_Polynomial_Opoly(X10,X12),hAPP(c_Polynomial_Opoly(X10,X11),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pcompose) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X34,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X34,X34) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10))),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [X21,X19] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X19),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X21)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X19 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X21 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(fact_add__neg__neg,axiom,
! [X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless(X10,X13,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__nonpos__neg,axiom,
! [X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless(X10,X13,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__pos__pos,axiom,
! [X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X4,X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__nonneg__pos,axiom,
! [X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X4,X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X4,X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X4,X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_poly__bound__exists,axiom,
! [X12,X29] :
? [X74] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X74)
& ! [X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7),X29)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X12),X7)),X74) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__bound__exists) ).
fof(fact_add__gr__0,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X35))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_zpower__zpower,axiom,
! [X14,X8,X9] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X8)),X14) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_zmult__assoc,axiom,
! [X55,X52,X53] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X52)),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X52),X55)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X24,X33,X34] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_real__mult__assoc,axiom,
! [X55,X52,X53] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X53),X52)),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X52),X55)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_mult__neg__pos,axiom,
! [X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,X13,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,X13,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X4),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [X13,X4,X10] :
( class_Rings_Oordered__cancel__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_split__mult__neg__le,axiom,
! [X13,X4,X10] :
( class_Rings_Oordered__cancel__semiring(X10)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
& c_Orderings_Oord__class_Oless__eq(X10,X13,c_Groups_Ozero__class_Ozero(X10)) )
| ( c_Orderings_Oord__class_Oless__eq(X10,X4,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13) ) )
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [X13,X4,X10] :
( class_Rings_Oordered__cancel__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [X13,X4,X10] :
( class_Rings_Oordered__cancel__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X4),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_less__1__mult,axiom,
! [X33,X34,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X34)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X33)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_mult__pos__pos,axiom,
! [X13,X4,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [X13,X4,X10] :
( class_Rings_Oordered__cancel__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_split__mult__pos__le,axiom,
! [X13,X4,X10] :
( class_Rings_Oordered__ring(X10)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
& c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X13) )
| ( c_Orderings_Oord__class_Oless__eq(X10,X4,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless__eq(X10,X13,c_Groups_Ozero__class_Ozero(X10)) ) )
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__neg__neg,axiom,
! [X13,X4,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless(X10,X13,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [X13,X4,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_add__strict__right__mono,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),c_Groups_Oplus__class_Oplus(X10,X13,X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X18,X4),c_Groups_Oplus__class_Oplus(X10,X18,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_add__right__mono,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),c_Groups_Oplus__class_Oplus(X10,X13,X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X18,X4),c_Groups_Oplus__class_Oplus(X10,X18,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_dvd__div__mult__self,axiom,
! [X13,X4,X10] :
( class_Divides_Osemiring__div(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X4,X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Divides_Odiv__class_Odiv(X10,X13,X4)),X4) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__mult__self) ).
fof(fact_one__less__power,axiom,
! [X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X4)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_dvd__power__same,axiom,
! [X33,X8,X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X9,X8)
=> c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X33),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X8),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).
fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
! [X33,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X14),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,c_RealDef_Oreal(tc_Nat_Onat,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
fof(fact_pos__add__strict,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,X13,X18)
=> c_Orderings_Oord__class_Oless(X10,X13,c_Groups_Oplus__class_Oplus(X10,X4,X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__strict__increasing2,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless(X10,X13,X18)
=> c_Orderings_Oord__class_Oless(X10,X13,c_Groups_Oplus__class_Oplus(X10,X4,X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,X18)
=> c_Orderings_Oord__class_Oless(X10,X13,c_Groups_Oplus__class_Oplus(X10,X4,X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__increasing,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,X18)
=> c_Orderings_Oord__class_Oless__eq(X10,X13,c_Groups_Oplus__class_Oplus(X10,X4,X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X4,X13,X18,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,X4)
=> c_Orderings_Oord__class_Oless__eq(X10,X13,c_Groups_Oplus__class_Oplus(X10,X4,X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_le__imp__power__dvd,axiom,
! [X4,X33,X34,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X34),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).
fof(fact_zdvd__antisym__nonneg,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X34,X33)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X33,X34)
=> X34 = X33 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
fof(fact_real__minus__mult__self__le,axiom,
! [X9,X60] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X60),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X26,X25)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X24),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X24),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_zadd__left__mono,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,X26),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_diff__le__mono,axiom,
! [X41,X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X41),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X41)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [X41,X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,X33),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_add__le__mono1,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X24),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_real__add__left__mono,axiom,
! [X14,X8,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,X9),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_dvd__diff,axiom,
! [X14,X8,X9,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X9,X8)
=> ( c_Rings_Odvd__class_Odvd(X10,X9,X14)
=> c_Rings_Odvd__class_Odvd(X10,X9,c_Groups_Ominus__class_Ominus(X10,X8,X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).
fof(fact_dvd__add,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X4,X13)
=> ( c_Rings_Odvd__class_Odvd(X10,X4,X18)
=> c_Rings_Odvd__class_Odvd(X10,X4,c_Groups_Oplus__class_Oplus(X10,X13,X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).
fof(fact_div__add__self1,axiom,
! [X4,X13,X10] :
( class_Divides_Osemiring__div(X10)
=> ( X13 != c_Groups_Ozero__class_Ozero(X10)
=> c_Divides_Odiv__class_Odiv(X10,c_Groups_Oplus__class_Oplus(X10,X13,X4),X13) = c_Groups_Oplus__class_Oplus(X10,c_Divides_Odiv__class_Odiv(X10,X4,X13),c_Groups_Oone__class_Oone(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self1) ).
fof(fact_div__add__self2,axiom,
! [X4,X13,X10] :
( class_Divides_Osemiring__div(X10)
=> ( X13 != c_Groups_Ozero__class_Ozero(X10)
=> c_Divides_Odiv__class_Odiv(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),X13) = c_Groups_Oplus__class_Oplus(X10,c_Divides_Odiv__class_Odiv(X10,X4,X13),c_Groups_Oone__class_Oone(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self2) ).
fof(fact_div__nonneg__neg__le0,axiom,
! [X13,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X13),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).
fof(fact_div__nonpos__pos__le0,axiom,
! [X13,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X13),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X8,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_smult__dvd__iff,axiom,
! [X27,X20,X17,X10] :
( class_Fields_Ofield(X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X17,X20),X27)
<=> ( ( X17 = c_Groups_Ozero__class_Ozero(X10)
=> X27 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) )
& ( X17 != c_Groups_Ozero__class_Ozero(X10)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X20,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
fof(fact_dvd__smult__cancel,axiom,
! [X11,X4,X12,X10] :
( class_Fields_Ofield(X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X12,c_Polynomial_Osmult(X10,X4,X11))
=> ( X4 != c_Groups_Ozero__class_Ozero(X10)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X12,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__cancel) ).
fof(fact_dvd__smult__iff,axiom,
! [X27,X20,X17,X10] :
( class_Fields_Ofield(X10)
=> ( X17 != c_Groups_Ozero__class_Ozero(X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X20,c_Polynomial_Osmult(X10,X17,X27))
<=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X20,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).
fof(fact_eq__diff__iff,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X35)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X39) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X39)
<=> X36 = X35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_int__div__less__self,axiom,
! [X24,X9] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X9,X24),X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).
fof(fact_diff__less,axiom,
! [X34,X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> ( 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_Ominus__class_Ominus(tc_Nat_Onat,X34,X33),X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
fof(fact_natceiling__subtract,axiom,
! [X9,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4),X9)
=> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X9,c_RealDef_Oreal(tc_Nat_Onat,X4))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X9),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__subtract) ).
fof(fact_natfloor__subtract,axiom,
! [X9,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4),X9)
=> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X9,c_RealDef_Oreal(tc_Nat_Onat,X4))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X9),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__subtract) ).
fof(fact_smult__dvd__cancel,axiom,
! [X11,X12,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X4,X12),X11)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X12,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X17,X17))
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
file('/export/starexec/sandbox2/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,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X17,X17))
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_even__less__0__iff,axiom,
! [X17,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X17,X17),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X17,X17),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/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,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X17,X17),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/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,
! [X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),X18) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),X13) ),
file('/export/starexec/sandbox2/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,
! [X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),X18) = c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Oplus__class_Oplus(X10,X13,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Oab__semigroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),X18) = c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Oplus__class_Oplus(X10,X13,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X5,X18,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Oplus__class_Oplus(X10,X18,X5)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X18),X5) ),
file('/export/starexec/sandbox2/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,
! [X5,X18,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Oplus__class_Oplus(X10,X18,X5)) = c_Groups_Oplus__class_Oplus(X10,X18,c_Groups_Oplus__class_Oplus(X10,X4,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_real__0__less__add__iff,axiom,
! [X21,X19] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X19,X21))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X19),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
fof(fact_real__0__le__add__iff,axiom,
! [X21,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X19,X21))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X19),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
fof(fact_real__add__less__0__iff,axiom,
! [X21,X19] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X19,X21),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
fof(fact_real__add__le__0__iff,axiom,
! [X21,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X19,X21),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
fof(fact_less__iff__diff__less__0,axiom,
! [X15,X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X17,X15)
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ominus__class_Ominus(X10,X17,X15),c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_le__iff__diff__le__0,axiom,
! [X15,X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X17,X15)
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ominus__class_Ominus(X10,X17,X15),c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_smult__monom,axiom,
! [X33,X13,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,X4,c_Polynomial_Omonom(X10,X13,X33)) = c_Polynomial_Omonom(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__monom) ).
fof(fact_smult__smult,axiom,
! [X12,X13,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,X4,c_Polynomial_Osmult(X10,X13,X12)) = c_Polynomial_Osmult(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__smult) ).
fof(fact_dvd__diff__nat,axiom,
! [X33,X34,X24] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X34)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X33)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_real__mult__order,axiom,
! [X8,X9] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X8,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_le__cube,axiom,
! [X34] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X34))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
fof(fact_diff__eq__diff__less,axiom,
! [X46,X16,X15,X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Groups_Ominus__class_Ominus(X10,X17,X15) = c_Groups_Ominus__class_Ominus(X10,X16,X46)
=> ( c_Orderings_Oord__class_Oless(X10,X17,X15)
<=> c_Orderings_Oord__class_Oless(X10,X16,X46) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [X46,X16,X15,X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Groups_Ominus__class_Ominus(X10,X17,X15) = c_Groups_Ominus__class_Ominus(X10,X16,X46)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X17,X15)
<=> c_Orderings_Oord__class_Oless__eq(X10,X16,X46) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_dvd__mult__cancel2,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X36),X36)
<=> X35 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
fof(fact_dvd__mult__cancel1,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35),X36)
<=> X35 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
fof(fact_mult__le__mono1,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X42,X43,X45,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X43),X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X45),X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_diff__cancel,axiom,
! [X33,X34,X24] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X33)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [X33,X24,X34] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X24),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X24)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__commute,axiom,
! [X24,X25,X26] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X25),X24) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X24),X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(fact_diff__diff__left,axiom,
! [X24,X25,X26] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X25),X24) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_zadd__assoc,axiom,
! [X55,X52,X53] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X53,X52),X55) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X53,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X52,X55)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X24,X33,X34] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33),X24) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [X14,X8,X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X14)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X14,X8,X9] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X14)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_zless__add1__eq,axiom,
! [X28,X51] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,X28)
| X51 = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_add1__zle__eq,axiom,
! [X28,X51] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,c_Groups_Oone__class_Oone(tc_Int_Oint)),X28)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zle__diff1__eq,axiom,
! [X28,X51] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X51,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X28,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_zle__add1__eq__le,axiom,
! [X28,X51] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X51,X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_dvd__mult__left,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),X18)
=> c_Rings_Odvd__class_Odvd(X10,X4,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_dvd__mult__right,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13),X18)
=> c_Rings_Odvd__class_Odvd(X10,X13,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_less__bin__lemma,axiom,
! [X56,X39] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X39,X56)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X39,X56),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_real__le__eq__diff,axiom,
! [X21,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,X21)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X19,X21),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
fof(fact_zero__less__diff,axiom,
! [X36,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X36))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_less__add__eq__less,axiom,
! [X33,X34,X41,X24] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X41)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X41) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_natceiling__add,axiom,
! [X4,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_RealDef_Oreal(tc_Nat_Onat,X4))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X9),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add) ).
fof(fact_natfloor__add,axiom,
! [X4,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_RealDef_Oreal(tc_Nat_Onat,X4))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X9),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add) ).
fof(fact_add__lessD1,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X25),X24)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__leD1,axiom,
! [X33,X24,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X24),X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X33,X24,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X24),X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_dvd__reduce,axiom,
! [X35,X39] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X39,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X39))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X39,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).
fof(fact_real__of__nat__diff,axiom,
! [X34,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X34)
=> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X34),c_RealDef_Oreal(tc_Nat_Onat,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X21,X19,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X19)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X21)
=> ( c_Groups_Oplus__class_Oplus(X10,X19,X21) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X19 = c_Groups_Ozero__class_Ozero(X10)
& X21 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_dvd__neg__div,axiom,
! [X9,X8,X10] :
( class_Divides_Oring__div(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X8,X9)
=> c_Divides_Odiv__class_Odiv(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),X8) = c_Groups_Ouminus__class_Ouminus(X10,c_Divides_Odiv__class_Odiv(X10,X9,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__neg__div) ).
fof(fact_dvd__div__neg,axiom,
! [X9,X8,X10] :
( class_Divides_Oring__div(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X8,X9)
=> c_Divides_Odiv__class_Odiv(X10,X9,c_Groups_Ouminus__class_Ouminus(X10,X8)) = c_Groups_Ouminus__class_Ouminus(X10,c_Divides_Odiv__class_Odiv(X10,X9,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__neg) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [X35,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X35))
<=> ( X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X35,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X35))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
| X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_less__poly__def,axiom,
! [X21,X19,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X10),X19,X21)
<=> c_Polynomial_Opos__poly(X10,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X21,X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__poly__def) ).
fof(fact_less__eq__poly__def,axiom,
! [X21,X19,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X10),X19,X21)
<=> ( X19 = X21
| c_Polynomial_Opos__poly(X10,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X21,X19)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__poly__def) ).
fof(fact_offset__poly__single,axiom,
! [X31,X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,c_Polynomial_OpCons(X10,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X31) = c_Polynomial_OpCons(X10,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__single) ).
fof(fact_smult__dvd,axiom,
! [X4,X11,X12,X10] :
( class_Fields_Ofield(X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X12,X11)
=> ( X4 != c_Groups_Ozero__class_Ozero(X10)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X4,X12),X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd) ).
fof(fact_pos__poly__pCons,axiom,
! [X20,X17,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Polynomial_Opos__poly(X10,c_Polynomial_OpCons(X10,X17,X20))
<=> ( c_Polynomial_Opos__poly(X10,X20)
| ( X20 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
& c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
fof(fact_dvd__smult,axiom,
! [X4,X11,X12,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X12,X11)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X12,c_Polynomial_Osmult(X10,X4,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult) ).
fof(fact_power__inject__exp,axiom,
! [X35,X36,X17,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X17)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X17),X36) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X17),X35)
<=> X36 = X35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_less__natfloor,axiom,
! [X33,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X9,c_RealDef_Oreal(tc_Nat_Onat,X33))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X9),X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__natfloor) ).
fof(fact_natceiling__le__eq,axiom,
! [X17,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X19),X17)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,c_RealDef_Oreal(tc_Nat_Onat,X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
fof(fact_le__natfloor__eq,axiom,
! [X17,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_RComplete_Onatfloor(X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X17),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
fof(fact_zero__less__power,axiom,
! [X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_one__le__power,axiom,
! [X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),X4)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(fact_zero__le__power,axiom,
! [X33,X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(fact_natceiling__add__one,axiom,
! [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
fof(fact_natfloor__add__one,axiom,
! [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
fof(fact_odd__nonzero,axiom,
! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X14),X14) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [X8,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X9,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_power_Opower_Opower__0,axiom,
! [X17,X81,X82,X10] : hAPP(hAPP(c_Power_Opower_Opower(X10,X82,X81),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X82,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_le__imp__0__less,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_dvd__mult__div__cancel,axiom,
! [X13,X4,X10] :
( class_Divides_Osemiring__div(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X4,X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Divides_Odiv__class_Odiv(X10,X13,X4)) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).
fof(fact_dvd__power,axiom,
! [X9,X33,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
| X9 = c_Groups_Oone__class_Oone(X10) )
=> c_Rings_Odvd__class_Odvd(X10,X9,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power) ).
fof(fact_minus__poly__code_I2_J,axiom,
! [X12,X4,X22] :
( class_Groups_Oab__group__add(X22)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X22),c_Polynomial_OpCons(X22,X4,X12)) = c_Polynomial_OpCons(X22,c_Groups_Ouminus__class_Ouminus(X22,X4),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X22),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
fof(fact_minus__pCons,axiom,
! [X12,X4,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Polynomial_OpCons(X10,X4,X12)) = c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__pCons) ).
fof(fact_dvd__mult2,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X4,X13)
=> c_Rings_Odvd__class_Odvd(X10,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).
fof(fact_dvd__mult,axiom,
! [X13,X18,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X4,X18)
=> c_Rings_Odvd__class_Odvd(X10,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).
fof(fact_norm__minus__commute,axiom,
! [X13,X4,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X4,X13)) = c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X13,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(fact_norm__mult,axiom,
! [X8,X9,X10] :
( class_RealVector_Oreal__normed__div__algebra(X10)
=> c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X8)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X9)),c_RealVector_Onorm__class_Onorm(X10,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).
fof(fact_zless__imp__add1__zle,axiom,
! [X14,X23] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Oone__class_Oone(tc_Int_Oint)),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_le__add__diff__inverse2,axiom,
! [X34,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X34)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33),X33) = X34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_diff__diff__cancel,axiom,
! [X33,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X33)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X26)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_le__add__diff__inverse,axiom,
! [X34,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X34)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33)) = X34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_le__funD,axiom,
! [X19,X1,X2,X10,X22] :
( class_Orderings_Oord(X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X22,hAPP(X2,X19),hAPP(X1,X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X19,X1,X2,X10,X22] :
( class_Orderings_Oord(X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X22,hAPP(X2,X19),hAPP(X1,X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_less__imp__diff__less,axiom,
! [X33,X24,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X33),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X14,X8,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X8)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X34,X25,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X8,X14,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X34,X25,X26] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X14,X8,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add1,axiom,
! [X34,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X8,X14,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_trans__le__add2,axiom,
! [X34,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_dvd__div__eq__mult,axiom,
! [X16,X15,X17,X10] :
( class_Divides_Osemiring__div(X10)
=> ( X17 != c_Groups_Ozero__class_Ozero(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X17,X15)
=> ( c_Divides_Odiv__class_Odiv(X10,X15,X17) = X16
<=> X15 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X17) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__eq__mult) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X35,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35)
<=> X36 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [X33,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_zdvd__mult__div__cancel,axiom,
! [X34,X33] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X33,X34)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X34,X33)) = X34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__div__cancel) ).
fof(fact_dvd__trans,axiom,
! [X18,X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X4,X13)
=> ( c_Rings_Odvd__class_Odvd(X10,X13,X18)
=> c_Rings_Odvd__class_Odvd(X10,X4,X18) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(fact_order__less__trans,axiom,
! [X14,X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> ( c_Orderings_Oord__class_Oless(X10,X8,X14)
=> c_Orderings_Oord__class_Oless(X10,X9,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X14,X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X8)
=> ( c_Orderings_Oord__class_Oless(X10,X8,X14)
=> c_Orderings_Oord__class_Oless(X10,X9,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X14,X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X14)
=> c_Orderings_Oord__class_Oless(X10,X9,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X14,X9,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X8,X9)
=> ( c_Orderings_Oord__class_Oless(X10,X14,X8)
=> c_Orderings_Oord__class_Oless(X10,X14,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_xt1_I8_J,axiom,
! [X14,X9,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X9)
=> ( c_Orderings_Oord__class_Oless(X10,X14,X8)
=> c_Orderings_Oord__class_Oless(X10,X14,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X14,X9,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X8,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X14,X8)
=> c_Orderings_Oord__class_Oless(X10,X14,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__trans,axiom,
! [X14,X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X8)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X14)
=> c_Orderings_Oord__class_Oless__eq(X10,X9,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X14,X9,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X14,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X14,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_Limits_Ominus__diff__minus,axiom,
! [X13,X4,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Groups_Ouminus__class_Ouminus(X10,X13)) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ominus__class_Ominus(X10,X4,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(fact_minus__add__distrib,axiom,
! [X13,X4,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Groups_Ouminus__class_Ouminus(X10,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [X13,X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X13),c_Groups_Ouminus__class_Ouminus(X10,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
fof(fact_real__natfloor__add__one__gt,axiom,
! [X9] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X9,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X9)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
fof(fact_neg__less__iff__less,axiom,
! [X17,X15,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X15),c_Groups_Ouminus__class_Ouminus(X10,X17))
<=> c_Orderings_Oord__class_Oless(X10,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_neg__le__iff__le,axiom,
! [X17,X15,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X15),c_Groups_Ouminus__class_Ouminus(X10,X17))
<=> c_Orderings_Oord__class_Oless__eq(X10,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_dvd__pos__nat,axiom,
! [X34,X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X34,X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).
fof(fact_div__pos__pos__trivial,axiom,
! [X13,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X13)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X13) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
fof(fact_zdiv__eq__0__iff,axiom,
! [X39,X38] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X38,X39) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( X39 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X38,X39) )
| ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X39,X38) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_div__neg__neg__trivial,axiom,
! [X13,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,X4)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X13) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
fof(fact_mult__left_Ominus,axiom,
! [X8,X9,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X9)),X8) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
fof(fact_mult_Ominus__left,axiom,
! [X13,X4,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X4)),X13) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_minus__mult__left,axiom,
! [X13,X4,X10] :
( class_Rings_Oring(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X4)),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
fof(fact_smult__minus__right,axiom,
! [X12,X4,X10] :
( class_Rings_Ocomm__ring(X10)
=> c_Polynomial_Osmult(X10,X4,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X12)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X4,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__right) ).
fof(fact_zdvd__imp__le,axiom,
! [X33,X14] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X14,X33)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
fof(fact_dvd__imp__le,axiom,
! [X33,X24] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X33)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
fof(fact_le__imp__diff__is__add,axiom,
! [X39,X40,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X40)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X38) = X39
<=> X40 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X38) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_norm__power,axiom,
! [X33,X9,X10] :
( class_RealVector_Oreal__normed__div__algebra(X10)
=> c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X9)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power) ).
fof(fact_add__minus__cancel,axiom,
! [X13,X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),X13)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_dvd_Oorder__trans,axiom,
! [X14,X8,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X14)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
fof(fact_zle__trans,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(fact_le__trans,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_real__le__trans,axiom,
! [X24,X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_pos__poly__mult,axiom,
! [X11,X12,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Polynomial_Opos__poly(X10,X12)
=> ( c_Polynomial_Opos__poly(X10,X11)
=> c_Polynomial_Opos__poly(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X12),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
fof(fact_real__of__nat__mult,axiom,
! [X33,X34] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X34)),c_RealDef_Oreal(tc_Nat_Onat,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
fof(fact_poly__minus,axiom,
! [X9,X12,X10] :
( class_Rings_Ocomm__ring(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X12)),X9) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(c_Polynomial_Opoly(X10,X12),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
fof(fact_minus__less__iff,axiom,
! [X15,X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),X15)
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X15),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(fact_minus__le__iff,axiom,
! [X15,X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),X15)
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X15),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).
fof(fact_less__minus__iff,axiom,
! [X15,X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ouminus__class_Ouminus(X10,X15))
<=> c_Orderings_Oord__class_Oless(X10,X15,c_Groups_Ouminus__class_Ouminus(X10,X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(fact_le__minus__iff,axiom,
! [X15,X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ouminus__class_Ouminus(X10,X15))
<=> c_Orderings_Oord__class_Oless__eq(X10,X15,c_Groups_Ouminus__class_Ouminus(X10,X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).
fof(fact_real__of__nat__add,axiom,
! [X33,X34] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X34),c_RealDef_Oreal(tc_Nat_Onat,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
fof(fact_zminus__zadd__distrib,axiom,
! [X23,X14] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X23)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_minus__monom,axiom,
! [X33,X4,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Polynomial_Omonom(X10,X4,X33)) = c_Polynomial_Omonom(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__monom) ).
fof(fact_smult__minus__left,axiom,
! [X12,X4,X10] :
( class_Rings_Ocomm__ring(X10)
=> c_Polynomial_Osmult(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),X12) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X4,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__left) ).
fof(fact_real__of__nat__less__iff,axiom,
! [X36,X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X35),c_RealDef_Oreal(tc_Nat_Onat,X36))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
fof(fact_real__of__nat__le__iff,axiom,
! [X36,X35] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X35),c_RealDef_Oreal(tc_Nat_Onat,X36))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_neg__less__0__iff__less,axiom,
! [X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_neg__le__0__iff__le,axiom,
! [X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_neg__0__less__iff__less,axiom,
! [X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Ouminus__class_Ouminus(X10,X17))
<=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_neg__0__le__iff__le,axiom,
! [X17,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Ouminus__class_Ouminus(X10,X17))
<=> c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_mult__right_Ominus,axiom,
! [X9,X49,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X49),c_Groups_Ouminus__class_Ouminus(X10,X9)) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X49),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_mult_Ominus__right,axiom,
! [X13,X4,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Ouminus__class_Ouminus(X10,X13)) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
fof(fact_minus__mult__right,axiom,
! [X13,X4,X10] :
( class_Rings_Oring(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Ouminus__class_Ouminus(X10,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
fof(fact_le__imp__neg__le,axiom,
! [X13,X4,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X13),c_Groups_Ouminus__class_Ouminus(X10,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_zero__less__two,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_real__natfloor__gt__diff__one,axiom,
! [X9] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X9,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X9))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).
fof(fact_minus__add__cancel,axiom,
! [X13,X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Groups_Oplus__class_Oplus(X10,X4,X13)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_neg__less__nonneg,axiom,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),X17)
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_minus__le__self__iff,axiom,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),X17)
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_less__minus__self__iff,axiom,
! [X17,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ouminus__class_Ouminus(X10,X17))
<=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_le__minus__self__iff,axiom,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ouminus__class_Ouminus(X10,X17))
<=> c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_power__real__of__nat,axiom,
! [X33,X34] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X34)),X33) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X34),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
fof(fact_zmult__zminus,axiom,
! [X23,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14)),X23) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
fof(fact_real__of__nat__power,axiom,
! [X33,X34] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X34),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X34)),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
fof(fact_nat__less__cases,axiom,
! [X64,X35,X36] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35)
=> hBOOL(hAPP(hAPP(X64,X35),X36)) )
=> ( ( X36 = X35
=> hBOOL(hAPP(hAPP(X64,X35),X36)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X36)
=> hBOOL(hAPP(hAPP(X64,X35),X36)) )
=> hBOOL(hAPP(hAPP(X64,X35),X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_synthetic__div__unique__lemma,axiom,
! [X4,X12,X18,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> ( c_Polynomial_Osmult(X10,X18,X12) = c_Polynomial_OpCons(X10,X4,X12)
=> X12 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
fof(fact_minus__mult__minus,axiom,
! [X13,X4,X10] :
( class_Rings_Oring(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X4)),c_Groups_Ouminus__class_Ouminus(X10,X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [X13,X4,X10] :
( class_Rings_Oring(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X4)),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Ouminus__class_Ouminus(X10,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_minus__dvd__iff,axiom,
! [X21,X19,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,c_Groups_Ouminus__class_Ouminus(X10,X19),X21)
<=> c_Rings_Odvd__class_Odvd(X10,X19,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_dvd__minus__iff,axiom,
! [X21,X19,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X19,c_Groups_Ouminus__class_Ouminus(X10,X21))
<=> c_Rings_Odvd__class_Odvd(X10,X19,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_square__eq__iff,axiom,
! [X15,X17,X10] :
( class_Rings_Oidom(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X15)
<=> ( X17 = X15
| X17 = c_Groups_Ouminus__class_Ouminus(X10,X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
fof(fact_pos__poly__add,axiom,
! [X11,X12,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Polynomial_Opos__poly(X10,X12)
=> ( c_Polynomial_Opos__poly(X10,X11)
=> c_Polynomial_Opos__poly(X10,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X12,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__add) ).
fof(fact_diff__eq__diff__eq,axiom,
! [X46,X16,X15,X17,X10] :
( class_Groups_Oab__group__add(X10)
=> ( c_Groups_Ominus__class_Ominus(X10,X17,X15) = c_Groups_Ominus__class_Ominus(X10,X16,X46)
=> ( X17 = X15
<=> X16 = X46 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_natfloor__power,axiom,
! [X33,X9] :
( X9 = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X9))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X9),X33)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X9)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__power) ).
fof(fact_minus__diff__eq,axiom,
! [X13,X4,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ominus__class_Ominus(X10,X4,X13)) = c_Groups_Ominus__class_Ominus(X10,X13,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_order__eq__iff,axiom,
! [X21,X19,X10] :
( class_Orderings_Oorder(X10)
=> ( X19 = X21
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
& c_Orderings_Oord__class_Oless__eq(X10,X21,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__antisym__conv,axiom,
! [X19,X21,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X21,X19)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
<=> X19 = X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X8,X9,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X8)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X9)
=> X9 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X9,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X9)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X8)
=> X9 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
! [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X35))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
fof(fact_less__add__one,axiom,
! [X4,X10] :
( class_Rings_Olinordered__semidom(X10)
=> c_Orderings_Oord__class_Oless(X10,X4,c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Oone__class_Oone(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_pCons__eq__iff,axiom,
! [X27,X15,X20,X17,X10] :
( class_Groups_Ozero(X10)
=> ( c_Polynomial_OpCons(X10,X17,X20) = c_Polynomial_OpCons(X10,X15,X27)
<=> ( X17 = X15
& X20 = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
fof(fact_monom__eq__iff,axiom,
! [X15,X35,X17,X10] :
( class_Groups_Ozero(X10)
=> ( c_Polynomial_Omonom(X10,X17,X35) = c_Polynomial_Omonom(X10,X15,X35)
<=> X17 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
fof(fact_add__right__cancel,axiom,
! [X16,X17,X15,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X15,X17) = c_Groups_Oplus__class_Oplus(X10,X16,X17)
<=> X15 = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__right__imp__eq,axiom,
! [X18,X4,X13,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X13,X4) = c_Groups_Oplus__class_Oplus(X10,X18,X4)
=> X13 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Ocancel__ab__semigroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X4,X13) = c_Groups_Oplus__class_Oplus(X10,X4,X18)
=> X13 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X16,X15,X17,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X17,X15) = c_Groups_Oplus__class_Oplus(X10,X17,X16)
<=> X15 = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [X18,X13,X4,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X4,X13) = c_Groups_Oplus__class_Oplus(X10,X4,X18)
=> X13 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_natceiling__le,axiom,
! [X4,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,c_RealDef_Oreal(tc_Nat_Onat,X4))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X9),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le) ).
fof(fact_le__natfloor,axiom,
! [X4,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X9),X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_RComplete_Onatfloor(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor) ).
fof(fact_order__root,axiom,
! [X17,X20,X10] :
( class_Rings_Oidom(X10)
=> ( hAPP(c_Polynomial_Opoly(X10,X20),X17) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X20 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
| c_Polynomial_Oorder(X10,X17,X20) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
fof(fact_diffs0__imp__equal,axiom,
! [X33,X34] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X34) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X34 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_real__natfloor__le,axiom,
! [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X9)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
fof(fact_uminus__dvd__conv_I1_J,axiom,
! [X83,X46] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X46,X83)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X46),X83) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
fof(fact_uminus__dvd__conv_I2_J,axiom,
! [X83,X46] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X46,X83)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X46,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X83)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
fof(fact_zero__le__square,axiom,
! [X4,X10] :
( class_Rings_Olinordered__ring(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(fact_dvd_Oantisym,axiom,
! [X8,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X9)
=> X9 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
fof(fact_dvd__antisym,axiom,
! [X33,X34] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X34,X33)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X33,X34)
=> X34 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__antisym) ).
fof(fact_dvd_Oantisym__conv,axiom,
! [X19,X21] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X19)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X21)
<=> X19 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
fof(fact_dvd_Oeq__iff,axiom,
! [X21,X19] :
( X19 = X21
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X21)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
fof(fact_zle__antisym,axiom,
! [X23,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14,X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X14)
=> X14 = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(fact_le__antisym,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X34)
=> X34 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_real__le__antisym,axiom,
! [X23,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X14)
=> X14 = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_add__diff__cancel,axiom,
! [X13,X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,c_Groups_Oplus__class_Oplus(X10,X4,X13),X13) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X13,X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ominus__class_Ominus(X10,X4,X13),X13) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X35) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X35 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_nat__add__right__cancel,axiom,
! [X35,X39,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X39) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X39)
<=> X36 = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X35,X36,X39] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X35)
<=> X36 = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_dvd__triv__left,axiom,
! [X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Rings_Odvd__class_Odvd(X10,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_dvd__triv__right,axiom,
! [X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Rings_Odvd__class_Odvd(X10,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(fact_le__Suc__ex__iff,axiom,
! [X56,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X56)
<=> ? [X57] : X56 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_le__iff__add,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35)
<=> ? [X37] : X35 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_diff__add__0,axiom,
! [X34,X33] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__add__inverse,axiom,
! [X34,X33] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34),X33) = X34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [X33,X34] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33),X33) = X34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_diff__le__self,axiom,
! [X33,X34] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33),X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(fact_le__add1,axiom,
! [X34,X33] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X34,X33] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_le__natfloor__eq__one,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_natceiling__le__eq__one,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X19),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
fof(fact_mult__cancel2,axiom,
! [X35,X39,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X39) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X39)
<=> ( X36 = X35
| X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(fact_real__mult__right__cancel,axiom,
! [X15,X17,X16] :
( X16 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X16)
<=> X17 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [X35,X36,X39] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35)
<=> ( X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X36 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_mult__cancel1,axiom,
! [X35,X36,X39] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35)
<=> ( X36 = X35
| X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_real__mult__left__cancel,axiom,
! [X15,X17,X16] :
( X16 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X15)
<=> X17 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
fof(fact_tsub__eq,axiom,
! [X9,X8] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X9)
=> c_Nat__Transfer_Otsub(X9,X8) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__eq) ).
fof(fact_order__less__le,axiom,
! [X21,X19,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
& X19 != X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_order__le__less,axiom,
! [X21,X19,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
<=> ( c_Orderings_Oord__class_Oless(X10,X19,X21)
| X19 = X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__neq__le__trans,axiom,
! [X13,X4,X10] :
( class_Orderings_Oorder(X10)
=> ( X4 != X13
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> c_Orderings_Oord__class_Oless(X10,X4,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X8,X9,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X8)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
| X9 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [X13,X4,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X4,X13)
=> ( X4 != X13
=> c_Orderings_Oord__class_Oless(X10,X4,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [X4,X13,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,X4)
=> ( X4 != X13
=> c_Orderings_Oord__class_Oless(X10,X13,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_xt1_I12_J,axiom,
! [X13,X4,X10] :
( class_Orderings_Oorder(X10)
=> ( X4 != X13
=> ( c_Orderings_Oord__class_Oless__eq(X10,X13,X4)
=> c_Orderings_Oord__class_Oless(X10,X13,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [X9,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10))),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_natceiling__mono,axiom,
! [X8,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X9),c_RComplete_Onatceiling(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__mono) ).
fof(fact_natfloor__mono,axiom,
! [X8,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X9),c_RComplete_Onatfloor(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).
fof(fact_order__less__imp__le,axiom,
! [X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X9,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_dvdI,axiom,
! [X24,X13,X4,X10] :
( class_Rings_Odvd(X10)
=> ( X4 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X24)
=> c_Rings_Odvd__class_Odvd(X10,X13,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [X28] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X28)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zero__less__norm__iff,axiom,
! [X19,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X19))
<=> X19 != c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_complex__mod__minus__le__complex__mod,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact_le__square,axiom,
! [X34] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X34)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
fof(fact_diff__minus__eq__add,axiom,
! [X13,X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,X4,c_Groups_Ouminus__class_Ouminus(X10,X13)) = c_Groups_Oplus__class_Oplus(X10,X4,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [X8,X9,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> c_Groups_Ominus__class_Ominus(X10,X9,X8) = c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Ouminus__class_Ouminus(X10,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_diff__def,axiom,
! [X13,X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,X4,X13) = c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Ouminus__class_Ouminus(X10,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).
fof(fact_ab__diff__minus,axiom,
! [X13,X4,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,X4,X13) = c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Ouminus__class_Ouminus(X10,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_norm__le__zero__iff,axiom,
! [X19,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X19 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
fof(fact_diff__is__0__eq,axiom,
! [X35,X36] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X35) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_zless__le,axiom,
! [X51,X28] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X51)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,X51)
& X28 != X51 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_le__neq__implies__less,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> ( X34 != X33
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35)
| X36 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__less__le,axiom,
! [X35,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35)
& X36 != X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_less__eq__real__def,axiom,
! [X21,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,X21)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X19,X21)
| X19 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_real__less__def,axiom,
! [X21,X19] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X19,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,X21)
& X19 != X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(fact_diff__is__0__eq_H,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_complex__i__mult__minus,axiom,
! [X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X9)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__mult__minus) ).
fof(fact_monom__0,axiom,
! [X4,X10] :
( class_Groups_Ozero(X10)
=> c_Polynomial_Omonom(X10,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X10,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__0) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X8,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X33,X34] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
| X34 = X33 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_less__imp__le__nat,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_real__of__nat__one,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__one) ).
fof(fact_mult__poly__0__left,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X11) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
fof(fact_diff__int__def__symmetric,axiom,
! [X23,X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [X23,X14] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,X23) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).
fof(fact_minus__real__def,axiom,
! [X8,X9] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X9,X8) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(fact_real__diff__def,axiom,
! [X66,X29] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X29,X66) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X29,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X66)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(fact_complex__diff__def,axiom,
! [X8,X9] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X9,X8) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X9,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff__def) ).
fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
! [X35] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X35),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_smult__eq__0__iff,axiom,
! [X20,X17,X10] :
( class_Rings_Oidom(X10)
=> ( c_Polynomial_Osmult(X10,X17,X20) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
<=> ( X17 = c_Groups_Ozero__class_Ozero(X10)
| X20 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
fof(fact_real__add__minus__iff,axiom,
! [X17,X19] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X19,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X17)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X19 = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_power__eq__0__iff,axiom,
! [X35,X17,X10] :
( ( class_Power_Opower(X10)
& class_Rings_Omult__zero(X10)
& class_Rings_Ono__zero__divisors(X10)
& class_Rings_Ozero__neq__one(X10) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X17),X35) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X17 = c_Groups_Ozero__class_Ozero(X10)
& X35 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_square__eq__1__iff,axiom,
! [X19,X10] :
( class_Rings_Oring__1__no__zero__divisors(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X19),X19) = c_Groups_Oone__class_Oone(X10)
<=> ( X19 = c_Groups_Oone__class_Oone(X10)
| X19 = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_pCons__eq__0__iff,axiom,
! [X20,X17,X10] :
( class_Groups_Ozero(X10)
=> ( c_Polynomial_OpCons(X10,X17,X20) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
<=> ( X17 = c_Groups_Ozero__class_Ozero(X10)
& X20 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(fact_offset__poly__eq__0__iff,axiom,
! [X32,X20,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X20,X32) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
<=> X20 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
fof(fact_linorder__neq__iff,axiom,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( X19 != X21
<=> ( c_Orderings_Oord__class_Oless(X10,X19,X21)
| c_Orderings_Oord__class_Oless(X10,X21,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
| X9 = X8
| c_Orderings_Oord__class_Oless(X10,X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_linorder__le__less__linear,axiom,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X8)
| c_Orderings_Oord__class_Oless(X10,X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_linorder__linear,axiom,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X8)
| c_Orderings_Oord__class_Oless__eq(X10,X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X18,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X4,X18) = c_Groups_Oplus__class_Oplus(X10,X18,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_minus__unique,axiom,
! [X13,X4,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X4,X13) = c_Groups_Ozero__class_Ozero(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,X4) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [X15,X17,X10] :
( class_Groups_Ogroup__add(X10)
=> ( X17 = c_Groups_Ouminus__class_Ouminus(X10,X15)
<=> c_Groups_Oplus__class_Oplus(X10,X17,X15) = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_add__eq__0__iff,axiom,
! [X21,X19,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X19,X21) = c_Groups_Ozero__class_Ozero(X10)
<=> X21 = c_Groups_Ouminus__class_Ouminus(X10,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
fof(fact_monom__eq__0__iff,axiom,
! [X35,X17,X10] :
( class_Groups_Ozero(X10)
=> ( c_Polynomial_Omonom(X10,X17,X35) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
<=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
fof(fact_mult__poly__0__right,axiom,
! [X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X12),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X13,X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_zless__linear,axiom,
! [X8,X9] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X8)
| X9 = X8
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X35,X36] :
( X36 != X35
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_dvd__0__left,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,c_Groups_Ozero__class_Ozero(X10),X4)
=> X4 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(fact_zle__linear,axiom,
! [X23,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14,X23)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(fact_nat__le__linear,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_real__le__linear,axiom,
! [X23,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X23)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_mult__eq__0__iff,axiom,
! [X15,X17,X10] :
( class_Rings_Oring__no__zero__divisors(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X17),X15) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X17 = c_Groups_Ozero__class_Ozero(X10)
| X15 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_no__zero__divisors,axiom,
! [X13,X4,X10] :
( class_Rings_Ono__zero__divisors(X10)
=> ( X4 != c_Groups_Ozero__class_Ozero(X10)
=> ( X13 != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13) != c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_divisors__zero,axiom,
! [X13,X4,X10] :
( class_Rings_Ono__zero__divisors(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X13) = c_Groups_Ozero__class_Ozero(X10)
=> ( X4 = c_Groups_Ozero__class_Ozero(X10)
| X13 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_diff__poly__code_I1_J,axiom,
! [X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X11) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(fact_zadd__commute,axiom,
! [X23,X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X23) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X33,X34] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_double__eq__0__iff,axiom,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X17,X17) = c_Groups_Ozero__class_Ozero(X10)
<=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Groups_Ozero__class_Ozero(X10) = c_Groups_Oplus__class_Oplus(X10,X17,X17)
<=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_right__minus__eq,axiom,
! [X15,X17,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ominus__class_Ominus(X10,X17,X15) = c_Groups_Ozero__class_Ozero(X10)
<=> X17 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [X15,X17,X10] :
( class_Groups_Oab__group__add(X10)
=> ( X17 = X15
<=> c_Groups_Ominus__class_Ominus(X10,X17,X15) = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_field__power__not__zero,axiom,
! [X33,X4,X10] :
( class_Rings_Oring__1__no__zero__divisors(X10)
=> ( X4 != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),X33) != c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_real__add__eq__0__iff,axiom,
! [X21,X19] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X19,X21) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X21 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(fact_add__0__iff,axiom,
! [X17,X15,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( X15 = c_Groups_Oplus__class_Oplus(X10,X15,X17)
<=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_poly__zero,axiom,
! [X20,X10] :
( ( class_Int_Oring__char__0(X10)
& class_Rings_Oidom(X10) )
=> ( c_Polynomial_Opoly(X10,X20) = c_Polynomial_Opoly(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)))
<=> X20 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).
fof(fact_less__imp__neq,axiom,
! [X8,X9,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> X9 != X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X8,X9,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> X9 != X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X8,X9,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> X8 != X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_pCons__0__0,axiom,
! [X10] :
( class_Groups_Ozero(X10)
=> c_Polynomial_OpCons(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).
fof(fact_one__poly__def,axiom,
! [X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X10)) = c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(fact_natceiling__neg,axiom,
! [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatceiling(X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__neg) ).
fof(fact_natfloor__neg,axiom,
! [X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatfloor(X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__neg) ).
fof(fact_neq0__conv,axiom,
! [X35] :
( X35 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_nat__dvd__1__iff__1,axiom,
! [X36] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(fact_le__0__eq,axiom,
! [X35] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_zmult__commute,axiom,
! [X23,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X33,X34] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_real__mult__commute,axiom,
! [X23,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_left__minus,axiom,
! [X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),X4) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
fof(fact_ab__left__minus,axiom,
! [X4,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),X4) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(fact_right__minus,axiom,
! [X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Ouminus__class_Ouminus(X10,X4)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
fof(fact_add__is__0,axiom,
! [X35,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X35) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_pcompose__0,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Opcompose(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X11) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__0) ).
fof(fact_synthetic__div__0,axiom,
! [X18,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osynthetic__div(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X18) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
fof(fact_offset__poly__0,axiom,
! [X31,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X31) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__0) ).
fof(fact_smult__0__right,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(fact_gr__implies__not0,axiom,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_norm__ge__zero,axiom,
! [X9,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(fact_power__0__left,axiom,
! [X33,X10] :
( ( class_Power_Opower(X10)
& class_Rings_Osemiring__0(X10) )
=> ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ozero__class_Ozero(X10)),X33) = c_Groups_Oone__class_Oone(X10) )
& ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ozero__class_Ozero(X10)),X33) = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(fact_add__eq__self__zero,axiom,
! [X33,X34] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X33) = X34
=> X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_real__natceiling__ge,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X9))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
fof(fact_poly__1,axiom,
! [X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X10))),X9) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).
fof(fact_poly__0,axiom,
! [X9,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X9) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(fact_less__not__refl2,axiom,
! [X34,X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X34)
=> X34 != X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__not__refl3,axiom,
! [X65,X66] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X66,X65)
=> X66 != X65 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X11,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X11) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_diff__poly__code_I2_J,axiom,
! [X12,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X12,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(fact_add__poly__code_I2_J,axiom,
! [X12,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X12,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_pos__poly__total,axiom,
! [X12,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( X12 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
| c_Polynomial_Opos__poly(X10,X12)
| c_Polynomial_Opos__poly(X10,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__total) ).
fof(fact_mult__is__0,axiom,
! [X35,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [X33,X34] :
( X34 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)
=> ( X33 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_diff__0,axiom,
! [X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,c_Groups_Ozero__class_Ozero(X10),X4) = c_Groups_Ouminus__class_Ouminus(X10,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [X35,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X35 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [X35,X36] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X35 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [X33] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14),X14) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_monom__eq__0,axiom,
! [X33,X10] :
( class_Groups_Ozero(X10)
=> c_Polynomial_Omonom(X10,c_Groups_Ozero__class_Ozero(X10),X33) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0) ).
fof(fact_smult__0__left,axiom,
! [X12,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,c_Groups_Ozero__class_Ozero(X10),X12) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(fact_power__power__power,axiom,
! [X10] :
( class_Power_Opower(X10)
=> c_Power_Opower__class_Opower(X10) = c_Power_Opower_Opower(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Otimes__class_Otimes(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(fact_power__one,axiom,
! [X33,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Oone__class_Oone(X10)),X33) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_mult__zero__left,axiom,
! [X4,X10] :
( class_Rings_Omult__zero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ozero__class_Ozero(X10)),X4) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_mult__left_Ozero,axiom,
! [X8,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ozero__class_Ozero(X10)),X8) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_mult_Ozero__left,axiom,
! [X13,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ozero__class_Ozero(X10)),X13) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ozero__class_Ozero(X10)),X4) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_zero__less__one,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oone__class_Oone(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_zero__le__one,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oone__class_Oone(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_mult__1__left,axiom,
! [X4,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oone__class_Oone(X10)),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_mult__1,axiom,
! [X4,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oone__class_Oone(X10)),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oone__class_Oone(X10)),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_mult__zero__right,axiom,
! [X4,X10] :
( class_Rings_Omult__zero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_mult__right_Ozero,axiom,
! [X9,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_mult_Ozero__right,axiom,
! [X4,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_smult__1__left,axiom,
! [X12,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Polynomial_Osmult(X10,c_Groups_Oone__class_Oone(X10),X12) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0__left,axiom,
! [X4,X10] :
( class_Groups_Omonoid__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [X4,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_diff__0__right,axiom,
! [X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,X4,c_Groups_Ozero__class_Ozero(X10)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Ozero__class_Ozero(X10)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add__0__right,axiom,
! [X4,X10] :
( class_Groups_Omonoid__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Ozero__class_Ozero(X10)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X4,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,X4,c_Groups_Ozero__class_Ozero(X10)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_one__dvd,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Rings_Odvd__class_Odvd(X10,c_Groups_Oone__class_Oone(X10),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(fact_dvd__0__right,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Rings_Odvd__class_Odvd(X10,X4,c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(fact_power__0,axiom,
! [X4,X10] :
( class_Power_Opower(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_mult__1__right,axiom,
! [X4,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Oone__class_Oone(X10)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X4,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Oone__class_Oone(X10)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),c_Groups_Oone__class_Oone(X10)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_diff__self,axiom,
! [X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,X4,X4) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_order__eq__refl,axiom,
! [X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( X9 = X8
=> c_Orderings_Oord__class_Oless__eq(X10,X9,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_power__one__right,axiom,
! [X4,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X9,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_zero__le__natceiling,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
fof(fact_zero__le__natfloor,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
fof(fact_dvd__refl,axiom,
! [X4,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Rings_Odvd__class_Odvd(X10,X4,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(fact_order__refl,axiom,
! [X9,X10] :
( class_Orderings_Opreorder(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,X9,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(fact_norm__minus__cancel,axiom,
! [X9,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)) = c_RealVector_Onorm__class_Onorm(X10,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
fof(fact_poly__eq__iff,axiom,
! [X27,X20,X10] :
( ( class_Int_Oring__char__0(X10)
& class_Rings_Oidom(X10) )
=> ( c_Polynomial_Opoly(X10,X20) = c_Polynomial_Opoly(X10,X27)
<=> X20 = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_gr0I,axiom,
! [X33] :
( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_diff__0__eq__0,axiom,
! [X33] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_zadd__0,axiom,
! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X33] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33) = X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X34] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_zadd__0__right,axiom,
! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X34] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_dvd_Oeq__refl,axiom,
! [X8,X9] :
( X9 = X8
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
fof(fact_eq__imp__le,axiom,
! [X33,X34] :
( X34 = X33
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
! [X9] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X33] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X33] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
! [X9] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
fof(fact_minus__poly__code_I1_J,axiom,
! [X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(fact_diff__self__eq__0,axiom,
! [X34] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X34) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_mult__0,axiom,
! [X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
fof(fact_neg__equal__iff__equal,axiom,
! [X15,X17,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ouminus__class_Ouminus(X10,X17) = c_Groups_Ouminus__class_Ouminus(X10,X15)
<=> X17 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_zmult__1,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_nat__mult__1,axiom,
! [X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33) = X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_real__mult__1,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X14) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_dvd_Oorder__refl,axiom,
! [X9] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(fact_zle__refl,axiom,
! [X23] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(fact_le__refl,axiom,
! [X33] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_real__le__refl,axiom,
! [X23] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(fact_mult__0__right,axiom,
! [X34] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(fact_zmult__1__right,axiom,
! [X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_minus__minus,axiom,
! [X4,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ouminus__class_Ouminus(X10,X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_minus__equation__iff,axiom,
! [X15,X17,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ouminus__class_Ouminus(X10,X17) = X15
<=> c_Groups_Ouminus__class_Ouminus(X10,X15) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_equation__minus__iff,axiom,
! [X15,X17,X10] :
( class_Groups_Ogroup__add(X10)
=> ( X17 = c_Groups_Ouminus__class_Ouminus(X10,X15)
<=> X15 = c_Groups_Ouminus__class_Ouminus(X10,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_psize__eq__0__iff,axiom,
! [X20,X10] :
( class_Groups_Ozero(X10)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X10,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X20 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_real__of__nat__inject,axiom,
! [X36,X35] :
( c_RealDef_Oreal(tc_Nat_Onat,X35) = c_RealDef_Oreal(tc_Nat_Onat,X36)
<=> X35 = X36 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [X17,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ozero__class_Ozero(X10) = c_Groups_Ouminus__class_Ouminus(X10,X17)
<=> c_Groups_Ozero__class_Ozero(X10) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [X17,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ouminus__class_Ouminus(X10,X17) = c_Groups_Ozero__class_Ozero(X10)
<=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_norm__eq__zero,axiom,
! [X19,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_RealVector_Onorm__class_Onorm(X10,X19) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X19 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X89,X88] :
( class_Orderings_Oorder(X88)
=> class_Orderings_Oorder(tc_fun(X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X89,X88] :
( class_Orderings_Oord(X88)
=> class_Orderings_Oord(tc_fun(X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X89,X88] :
( class_Orderings_Opreorder(X88)
=> class_Orderings_Opreorder(tc_fun(X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(fact_zminus__zminus,axiom,
! [X14] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14)) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(fact_neg__equal__zero,axiom,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Groups_Ouminus__class_Ouminus(X10,X17) = X17
<=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_equal__neg__zero,axiom,
! [X17,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( X17 = c_Groups_Ouminus__class_Ouminus(X10,X17)
<=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(help_c__fequal__2,axiom,
! [X21,X19] :
( X19 != X21
| hBOOL(c_fequal(X19,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_minus__zero,axiom,
! [X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(fact_norm__one,axiom,
! [X10] :
( class_RealVector_Oreal__normed__algebra__1(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Groups_Oone__class_Oone(X10)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).
fof(fact_norm__zero,axiom,
! [X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(fact_natceiling__real__of__nat,axiom,
! [X33] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X33)) = X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
fof(fact_natfloor__real__of__nat,axiom,
! [X33] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X33)) = X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
fof(fact_real__of__nat__zero__iff,axiom,
! [X35] :
( c_RealDef_Oreal(tc_Nat_Onat,X35) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
fof(fact_zero__neq__one,axiom,
! [X10] :
( class_Rings_Ozero__neq__one(X10)
=> c_Groups_Ozero__class_Ozero(X10) != c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X10] :
( class_Rings_Ozero__neq__one(X10)
=> c_Groups_Oone__class_Oone(X10) != c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [X88] :
( class_Groups_Ocancel__comm__monoid__add(X88)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Divides_Oring__div,axiom,
! [X88] :
( class_Fields_Ofield(X88)
=> class_Divides_Oring__div(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).
fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
! [X88] :
( class_Fields_Ofield(X88)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Power_Opower(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
! [X88] :
( class_Rings_Oidom(X88)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
! [X88] :
( class_Rings_Ocomm__ring__1(X88)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
! [X88] :
( class_Rings_Ocomm__ring__1(X88)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Groups_Oone(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
! [X88] :
( class_Rings_Oidom(X88)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
! [X88] :
( class_Rings_Oidom(X88)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [X88] :
( class_Groups_Oab__group__add(X88)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [X88] :
( class_Rings_Ocomm__ring(X88)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [X88] :
( class_Groups_Oab__group__add(X88)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [X88] :
( class_Rings_Ocomm__ring(X88)
=> class_Rings_Oring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [X88] :
( class_Rings_Oidom(X88)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
! [X88] :
( class_Groups_Ocomm__monoid__add(X88)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
! [X88] :
( class_Groups_Ocancel__comm__monoid__add(X88)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
! [X88] :
( class_Groups_Ocancel__comm__monoid__add(X88)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [X88] :
( class_Rings_Oidom(X88)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [X88] :
( class_Groups_Ocomm__monoid__add(X88)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [X88] :
( class_Groups_Ozero(X88)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [X88] :
( class_Groups_Ocomm__monoid__add(X88)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(conj_1,conjecture,
v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(fact_pCons_Oprems,axiom,
c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons_Oprems) ).
fof(fact_int__0__less__1,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_i__mult__eq2,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_i__mult__eq2) ).
fof(fact_real__of__nat__1,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
fof(fact_zminus__0,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(fact_assms,axiom,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).
fof(fact_H,axiom,
v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H) ).
fof(fact_natceiling__one,axiom,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__one) ).
fof(fact_natceiling__zero,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).
fof(fact_natfloor__one,axiom,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__one) ).
fof(fact_natfloor__zero,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__zero) ).
fof(fact_int__0__neq__1,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(fact_real__zero__not__eq__one,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_complex__i__not__one,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__one) ).
fof(fact_complex__i__not__zero,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).
fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Int__Oint__Divides_Oring__div,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(arity_Int__Oint__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(arity_Nat__Onat__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).
fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__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/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_RealDef__Oreal__Groups_Oone,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_RealDef__Oreal__Rings_Oring,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
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/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(i_0_1232,plain,
! [X4,X12,X10] :
( class_Rings_Oidom(X10)
=> ( X12 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
=> ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))))),c_Nat_OSuc(c_Polynomial_Oorder(X10,X4,X12))),X12) ) ),
inference(fof_simplification,[status(thm)],[fact_order__2]) ).
fof(i_0_1233,plain,
! [X4,X12,X10] :
( class_Rings_Oidom(X10)
=> ( X12 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))))),c_Polynomial_Oorder(X10,X4,X12)),X12)
& ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X4),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))))),c_Nat_OSuc(c_Polynomial_Oorder(X10,X4,X12))),X12) ) ) ),
inference(fof_simplification,[status(thm)],[fact_order]) ).
fof(i_0_1234,plain,
! [X33,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,c_Nat_OSuc(X33))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> X34 = c_Nat_OSuc(X33) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_1235,plain,
! [X35,X36] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X35)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X35),X36) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_1236,plain,
! [X35,X36] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,c_Nat_OSuc(X36)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_1237,plain,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,c_Nat_OSuc(X33))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> X34 = X33 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_1238,plain,
! [X34,X33] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X34)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Nat_OSuc(X34))
=> X34 = X33 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_1239,plain,
! [X36,X35] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X36)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,c_Nat_OSuc(X36))
<=> X35 = X36 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_1240,plain,
! [X33] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X33),X33),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_1241,plain,
! [X5224,X5225,X5226] :
( ~ class_Rings_Oidom(X5226)
| X5225 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5226))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5226),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5226)),c_Polynomial_OpCons(X5226,c_Groups_Ouminus__class_Ouminus(X5226,X5224),c_Polynomial_OpCons(X5226,c_Groups_Oone__class_Oone(X5226),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5226))))),c_Nat_OSuc(c_Polynomial_Oorder(X5226,X5224,X5225))),X5225) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1232])]) ).
fof(i_0_1242,plain,
! [X4855] : c_Nat_OSuc(X4855) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4855,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1243,plain,
! [X5347,X5348,X5349] :
( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5349),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5349)),c_Polynomial_OpCons(X5349,c_Groups_Ouminus__class_Ouminus(X5349,X5347),c_Polynomial_OpCons(X5349,c_Groups_Oone__class_Oone(X5349),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5349))))),c_Polynomial_Oorder(X5349,X5347,X5348)),X5348)
| X5348 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5349))
| ~ class_Rings_Oidom(X5349) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5349),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5349)),c_Polynomial_OpCons(X5349,c_Groups_Ouminus__class_Ouminus(X5349,X5347),c_Polynomial_OpCons(X5349,c_Groups_Oone__class_Oone(X5349),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5349))))),c_Nat_OSuc(c_Polynomial_Oorder(X5349,X5347,X5348))),X5348)
| X5348 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5349))
| ~ class_Rings_Oidom(X5349) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1233])])]) ).
fof(i_0_1244,plain,
! [X4734,X4735,X4736] :
( ~ class_Rings_Ocomm__ring__1(X4736)
| c_Groups_Ominus__class_Ominus(X4736,hAPP(hAPP(c_Power_Opower__class_Opower(X4736),X4735),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X4736),X4734),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4736),c_Groups_Ominus__class_Ominus(X4736,X4735,X4734)),c_Groups_Oplus__class_Oplus(X4736,X4735,X4734)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__two__diff])]) ).
fof(i_0_1245,plain,
! [X4840,X4841,X4842] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4842)),X4841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4842)),X4840))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4841,X4840) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4841,X4840)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4842)),X4841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4842)),X4840)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).
fof(i_0_1246,plain,
! [X4849,X4850,X4851] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4851)),X4850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4851)),X4849))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4850,X4849) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4850,X4849)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4851)),X4850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4851)),X4849)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).
fof(i_0_1247,plain,
! [X5616,X5617] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk35_2(X5616,X5617))),X5617),X5616)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5616)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5617) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5616,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk35_2(X5616,X5617)))),X5617))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5616)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5617) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reals__Archimedean4])])])]) ).
fof(i_0_1248,plain,
! [X5604,X5605,X5606,X5609,X5610,X5613] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5606)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5605,hAPP(X5604,esk30_3(X5604,X5605,X5606))),X5606)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5605,hAPP(X5604,X5609)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk31_2(X5604,X5605))))
| ~ class_RealVector_Oreal__normed__vector(X5605) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_2(X5604,X5605))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5605,hAPP(X5604,esk32_3(X5604,X5605,X5610))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X5610)))
| ~ class_RealVector_Oreal__normed__vector(X5605) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5605,hAPP(X5604,X5613)),esk33_2(X5604,X5605))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5605,hAPP(X5604,esk32_3(X5604,X5605,X5610))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X5610)))
| ~ class_RealVector_Oreal__normed__vector(X5605) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def2])])])])]) ).
fof(i_0_1249,plain,
! [X5594,X5595,X5596,X5599,X5600,X5603] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5596)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5595,hAPP(X5594,esk26_3(X5594,X5595,X5596))),X5596)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5595,hAPP(X5594,X5599)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk27_2(X5594,X5595))))
| ~ class_RealVector_Oreal__normed__vector(X5595) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk29_2(X5594,X5595))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5595,hAPP(X5594,esk28_3(X5594,X5595,X5600))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X5600)))
| ~ class_RealVector_Oreal__normed__vector(X5595) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5595,hAPP(X5594,X5603)),esk29_2(X5594,X5595))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5595,hAPP(X5594,esk28_3(X5594,X5595,X5600))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X5600)))
| ~ class_RealVector_Oreal__normed__vector(X5595) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def])])])])]) ).
fof(i_0_1250,plain,
! [X4535,X4536,X4537] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X4537),X4536),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X4537),X4535),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X4536 = X4535
| X4536 = c_Groups_Ouminus__class_Ouminus(X4537,X4535)
| ~ class_Rings_Oidom(X4537) )
& ( X4536 != X4535
| hAPP(hAPP(c_Power_Opower__class_Opower(X4537),X4536),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X4537),X4535),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X4537) )
& ( X4536 != c_Groups_Ouminus__class_Ouminus(X4537,X4535)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4537),X4536),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X4537),X4535),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X4537) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__two__disj])])]) ).
fof(i_0_1251,plain,
! [X5047,X5048,X5049,X5050] :
( ~ class_Rings_Olinordered__semidom(X5050)
| ~ c_Orderings_Oord__class_Oless__eq(X5050,hAPP(hAPP(c_Power_Opower__class_Opower(X5050),X5049),c_Nat_OSuc(X5048)),hAPP(hAPP(c_Power_Opower__class_Opower(X5050),X5047),c_Nat_OSuc(X5048)))
| ~ c_Orderings_Oord__class_Oless__eq(X5050,c_Groups_Ozero__class_Ozero(X5050),X5047)
| c_Orderings_Oord__class_Oless__eq(X5050,X5049,X5047) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base])]) ).
fof(i_0_1252,plain,
! [X4944,X4945,X4946,X4947] :
( ~ class_Groups_Omonoid__mult(X4947)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4946,X4945)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4947),X4944),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4945),X4946)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4947),hAPP(hAPP(c_Power_Opower__class_Opower(X4947),X4944),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4945,X4946))),X4944) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__realpow__diff])]) ).
fof(i_0_1253,plain,
! [X8,X9,X10] :
( class_Rings_Olinordered__ring(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X8)),c_Groups_Ozero__class_Ozero(X10)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_1254,plain,
! [X5216,X5217,X5218,X5219,X5220] : hAPP(hAPP(c_Power_Opower_Opower(X5220,X5219,X5218),X5217),c_Nat_OSuc(X5216)) = hAPP(hAPP(X5218,X5217),hAPP(hAPP(c_Power_Opower_Opower(X5220,X5219,X5218),X5217),X5216)),
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(i_0_1255,plain,
! [X4708,X4709,X4710] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4710)),X4709) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4710)),X4708)
| X4709 = X4708 )
& ( X4709 != X4708
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4710)),X4709) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4710)),X4708) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).
fof(i_0_1256,plain,
! [X4895,X4896] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4896)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4895)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4895),X4896)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).
fof(i_0_1257,plain,
! [X4900,X4901] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4901)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4901),X4900)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4900)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4901),X4900)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4901)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4900)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4901),X4900)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).
fof(i_0_1258,plain,
! [X4904,X4905,X4906] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4906,X4905)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4905,X4906)),X4904) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4905),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4906,X4904)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])]) ).
fof(i_0_1259,plain,
! [X4907,X4908,X4909] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4909,X4908)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4907,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4908,X4909))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4907,X4909),c_Nat_OSuc(X4908)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1])]) ).
fof(i_0_1260,plain,
! [X5043,X5044,X5045,X5046] :
( ~ class_Rings_Olinordered__semidom(X5046)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5046),X5045),c_Nat_OSuc(X5044)) != hAPP(hAPP(c_Power_Opower__class_Opower(X5046),X5043),c_Nat_OSuc(X5044))
| ~ c_Orderings_Oord__class_Oless__eq(X5046,c_Groups_Ozero__class_Ozero(X5046),X5045)
| ~ c_Orderings_Oord__class_Oless__eq(X5046,c_Groups_Ozero__class_Ozero(X5046),X5043)
| X5045 = X5043 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).
fof(i_0_1261,plain,
! [X5632,X5633] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5633)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5632)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5632),X5633),X5632) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5632),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5633,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__power__div__base])]) ).
fof(i_0_1262,plain,
! [X5110] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5110,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X5110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X5110 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__lt__two__imp__zero__or__one])]) ).
fof(i_0_1263,plain,
! [X15,X17,X64] :
( hBOOL(hAPP(X64,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X15)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X15)
& ~ hBOOL(hAPP(X64,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X68] :
( X17 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X68)
& ~ hBOOL(hAPP(X64,X68)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(i_0_1264,plain,
! [X4893,X4894] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4894)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4893)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4894,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4894),X4893)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).
fof(i_0_1265,plain,
! [X4891,X4892] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4892)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4891)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4892,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4891),X4892)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).
fof(i_0_1266,plain,
! [X4718,X4719,X4720] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4720),X4719),c_Nat_OSuc(X4718)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4720,X4719),X4718),
inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).
fof(i_0_1267,plain,
! [X5084,X5085,X5086] :
( ~ class_Rings_Olinordered__semidom(X5086)
| ~ c_Orderings_Oord__class_Oless(X5086,c_Groups_Ozero__class_Ozero(X5086),X5085)
| ~ c_Orderings_Oord__class_Oless(X5086,X5085,c_Groups_Oone__class_Oone(X5086))
| c_Orderings_Oord__class_Oless(X5086,hAPP(hAPP(c_Power_Opower__class_Opower(X5086),X5085),c_Nat_OSuc(X5084)),c_Groups_Oone__class_Oone(X5086)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).
fof(i_0_1268,plain,
! [X4726,X4727,X4728] :
( ~ class_Rings_Olinordered__semidom(X4728)
| ~ c_Orderings_Oord__class_Oless__eq(X4728,c_Groups_Ozero__class_Ozero(X4728),X4727)
| ~ c_Orderings_Oord__class_Oless__eq(X4728,X4727,c_Groups_Oone__class_Oone(X4728))
| c_Orderings_Oord__class_Oless__eq(X4728,hAPP(hAPP(c_Power_Opower__class_Opower(X4728),X4727),c_Nat_OSuc(X4726)),X4727) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__Suc__le__self])]) ).
fof(i_0_1269,plain,
! [X5037,X5038] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5038)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5038),X5037)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).
fof(i_0_1270,plain,
! [X5059,X5060,X5061] :
( ~ class_Rings_Olinordered__semidom(X5061)
| ~ c_Orderings_Oord__class_Oless(X5061,c_Groups_Oone__class_Oone(X5061),X5060)
| c_Orderings_Oord__class_Oless(X5061,c_Groups_Oone__class_Oone(X5061),hAPP(hAPP(c_Power_Opower__class_Opower(X5061),X5060),c_Nat_OSuc(X5059))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).
fof(i_0_1271,plain,
! [X4687,X4688] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X4688),c_Nat_OSuc(X4687))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4688,X4687) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_1272,plain,
! [X4670,X4671] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X4671),c_Nat_OSuc(X4670))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4671,X4670) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4671,X4670)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X4671),c_Nat_OSuc(X4670)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_1273,plain,
! [X4701,X4702] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4702),c_Nat_OSuc(X4701))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4702,X4701) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4702,X4701)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4702),c_Nat_OSuc(X4701)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_1274,plain,
! [X4897] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4897)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4897,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X4897 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).
fof(i_0_1275,plain,
! [X4898,X4899] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4899)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4899,c_Nat_OSuc(X4898)),X4899) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).
fof(i_0_1276,plain,
! [X35,X64] :
( ~ hBOOL(hAPP(X64,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X64,X35))
=> ? [X37] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X35)
& ! [X69] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X69,X37)
=> ~ hBOOL(hAPP(X64,X69)) )
& hBOOL(hAPP(X64,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).
fof(i_0_1277,plain,
! [X4497,X4498] :
( ( X4498 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4498,X4497) = X4497 )
& ( X4498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4498,X4497) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4498,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4497)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).
fof(i_0_1278,plain,
! [X4556,X4557,X4558] :
( ~ class_Rings_Ocomm__semiring__1(X4558)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4558),hAPP(hAPP(c_Power_Opower__class_Opower(X4558),X4557),X4556)),X4557) = hAPP(hAPP(c_Power_Opower__class_Opower(X4558),X4557),c_Nat_OSuc(X4556)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).
fof(i_0_1279,plain,
! [X5028,X5029,X5030] :
( ~ class_Groups_Omonoid__mult(X5030)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5030),X5029),c_Nat_OSuc(X5028)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5030),hAPP(hAPP(c_Power_Opower__class_Opower(X5030),X5029),X5028)),X5029) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).
fof(i_0_1280,plain,
! [X4847,X4848] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4848)),X4847) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4847,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4848),X4847)),
inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).
fof(i_0_1281,plain,
! [X4852,X4853] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4853,X4852)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4852),X4853) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4852,X4853)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).
fof(i_0_1282,plain,
! [X4824,X4825] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4825,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4825,X4824))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_1283,plain,
! [X4822,X4823] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4823,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4822,X4823))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_1284,plain,
! [X4703,X4704] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4704,c_Nat_OSuc(X4703))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4704,X4703)
| X4704 = c_Nat_OSuc(X4703) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4704,X4703)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4704,c_Nat_OSuc(X4703)) )
& ( X4704 != c_Nat_OSuc(X4703)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4704,c_Nat_OSuc(X4703)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_1285,plain,
! [X4697,X4698] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4698,c_Nat_OSuc(X4697))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4698,X4697)
| X4698 = c_Nat_OSuc(X4697) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1234])]) ).
fof(i_0_1286,plain,
! [X14,X8,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X9) )
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X8) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X9) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__trans]) ).
fof(i_0_1287,plain,
! [X4500,X4501] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4501,X4500)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X4501),c_Nat_OSuc(X4500)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_1288,plain,
! [X4800,X4801,X4803,X4804,X4805] :
( ( X4801 = c_Nat_OSuc(esk17_2(X4800,X4801))
| X4801 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4801,c_Nat_OSuc(X4800)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk17_2(X4800,X4801),X4800)
| X4801 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4801,c_Nat_OSuc(X4800)) )
& ( X4804 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4804,c_Nat_OSuc(X4803)) )
& ( X4804 != c_Nat_OSuc(X4805)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4805,X4803)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4804,c_Nat_OSuc(X4803)) ) ),
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_1289,plain,
! [X4836,X4837] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4836,c_Nat_OSuc(X4837))
| X4836 = X4837
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4837,X4836) )
& ( X4836 != X4837
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4836,c_Nat_OSuc(X4837))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4837,X4836) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_1290,plain,
! [X4705,X4706] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4706,X4705)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4705),X4706) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4705),X4706)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4706,X4705) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1235])]) ).
fof(i_0_1291,plain,
! [X4666,X4667] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4667,X4666)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4666,c_Nat_OSuc(X4667)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4666,c_Nat_OSuc(X4667))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4667,X4666) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1236])]) ).
fof(i_0_1292,plain,
! [X4930,X4931,X4932] :
( ~ class_Groups_Ozero(X4932)
| c_Polynomial_Omonom(X4932,X4931,c_Nat_OSuc(X4930)) = c_Polynomial_OpCons(X4932,c_Groups_Ozero__class_Ozero(X4932),c_Polynomial_Omonom(X4932,X4931,X4930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__Suc])]) ).
fof(i_0_1293,plain,
! [X4989] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X4989) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).
fof(i_0_1294,plain,
! [X4680,X4681,X4682] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4682,X4681)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4681,X4680)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X4682),X4680) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_1295,plain,
! [X5379] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5379,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X5379 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X5379 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5379,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1])]) ).
fof(i_0_1296,plain,
! [X4716,X4717] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4717),c_Nat_OSuc(X4716)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4717,X4716),
inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).
fof(i_0_1297,plain,
! [X4693,X4694] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X4694),X4693) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4694,c_Nat_OSuc(X4693)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_1298,plain,
! [X4858,X4859] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4859,c_Nat_OSuc(X4858)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4859,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4858),
inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).
fof(i_0_1299,plain,
! [X5025,X5026,X5027] :
( ~ class_Power_Opower(X5027)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5027),X5026),c_Nat_OSuc(X5025)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5027),X5026),hAPP(hAPP(c_Power_Opower__class_Opower(X5027),X5026),X5025)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).
fof(i_0_1300,plain,
! [X4550,X4551,X4552] :
( ~ class_Rings_Ocomm__semiring__1(X4552)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4552),X4551),c_Nat_OSuc(X4550)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4552),X4551),hAPP(hAPP(c_Power_Opower__class_Opower(X4552),X4551),X4550)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).
fof(i_0_1301,plain,
! [X4553,X4554,X4555] :
( ~ class_Rings_Ocomm__semiring__1(X4555)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4555),X4554),hAPP(hAPP(c_Power_Opower__class_Opower(X4555),X4554),X4553)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4555),X4554),c_Nat_OSuc(X4553)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).
fof(i_0_1302,plain,
! [X4691,X4692] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X4692),X4691) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4692,X4691)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_1303,plain,
! [X4689,X4690] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4690,c_Nat_OSuc(X4689)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4690,X4689)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_1304,plain,
! [X4683,X4684] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4684,c_Nat_OSuc(X4683))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4684,X4683)
| X4684 = X4683 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1237])]) ).
fof(i_0_1305,plain,
! [X4674,X4675] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4675,X4674)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4675,c_Nat_OSuc(X4674))
| X4674 = X4675 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1238])]) ).
fof(i_0_1306,plain,
! [X4672,X4673] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4673,c_Nat_OSuc(X4672))
| X4673 = X4672
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4673,X4672) )
& ( X4673 != X4672
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4673,c_Nat_OSuc(X4672))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4673,X4672) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1239])])]) ).
fof(i_0_1307,plain,
! [X4668,X4669] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4669,c_Nat_OSuc(X4668))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4669,X4668)
| X4669 = X4668 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4669,X4668)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4669,c_Nat_OSuc(X4668)) )
& ( X4669 != X4668
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4669,c_Nat_OSuc(X4668)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_1308,plain,
! [X4685,X4686] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X4686),X4685)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4686,X4685) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_1309,plain,
! [X4838,X4839] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4839),X4838)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4839,X4838) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_1310,plain,
! [X4830,X4831] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4831),X4830)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4831,X4830) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4831,X4830)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4831),X4830) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_1311,plain,
! [X4826,X4827] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4827,X4826)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4827),X4826) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4827),X4826)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4827,X4826) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_1312,plain,
! [X4695,X4696] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4696),X4695)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4696,X4695) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_1313,plain,
! [X4828,X4829] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4829,c_Nat_OSuc(X4828))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4829,X4828) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4829,X4828)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4829,c_Nat_OSuc(X4828)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_1314,plain,
! [X4816,X4817,X4819,X4820,X4821] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4817,X4816)
| X4816 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4817,esk18_2(X4816,X4817))) )
& ( X4819 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4820,X4821))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4820,X4819) ) ),
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_1315,plain,
! [X14,X8,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X8) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X9) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less__trans]) ).
fof(i_0_1316,plain,
! [X14,X8,X9] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X9) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X14)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X9) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le__trans]) ).
fof(i_0_1317,plain,
! [X4678,X4679] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4679,X4678)
| c_Nat_OSuc(X4679) = X4678
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X4679),X4678) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_1318,plain,
! [X33,X24,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X24),X33)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X33) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_1319,plain,
! [X4845,X4846] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4846),c_Nat_OSuc(X4845)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4846,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4846),X4845)),
inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).
fof(i_0_1320,plain,
! [X5537] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X5537))),
inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc__gt__zero]) ).
fof(i_0_1321,plain,
! [X4806,X4807] :
( ( X4807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4807 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4807,X4806) )
& ( X4806 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4807 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4807,X4806) )
& ( X4807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4807,X4806) )
& ( X4806 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4807,X4806) )
& ( X4807 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4806 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4807,X4806) )
& ( X4807 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4806 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4807,X4806) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_1322,plain,
! [X4808,X4809] :
( ( X4809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4809 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4809,X4808) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4808 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4809 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4809,X4808) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4809,X4808) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4808 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4809,X4808) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4809 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4808 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4809,X4808) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4809 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4808 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4809,X4808) = 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_1323,plain,
! [X1,X2,X10,X22] :
( class_Orderings_Oord(X22)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X10,X22),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_1324,plain,
! [X4814,X4815] :
( ( X4815 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4815),X4814) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4814 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4815),X4814) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4815 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4814 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4815),X4814) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff])])]) ).
fof(i_0_1325,plain,
! [X4799] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4799,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X4799 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4799 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4799,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_1326,plain,
! [X4843,X4844] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4844,X4843),c_Nat_OSuc(X4844)),
inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).
fof(i_0_1327,plain,
! [X4,X10] :
( class_Rings_Olinordered__ring(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X4),X4),c_Groups_Ozero__class_Ozero(X10)) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_1328,plain,
! [X33,X34] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X34)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X34,X33)
=> ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X33,X34) ) ),
inference(fof_simplification,[status(thm)],[fact_zdvd__not__zless]) ).
fof(i_0_1329,plain,
! [X33,X34] :
( 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,X34,X33)
=> ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X33,X34) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__dvd__not__less]) ).
fof(i_0_1330,plain,
! [X4707] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4707),X4707),
inference(variable_rename,[status(thm)],[i_0_1240]) ).
fof(i_0_1331,plain,
! [X4935] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4935)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4935,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X4935 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).
fof(i_0_1332,plain,
! [X4936] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4936)
| X4936 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4936,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred_H])]) ).
fof(i_0_1333,plain,
! [X4834,X4835] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4835,X4834)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4835),X4834) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_1334,plain,
! [X4676,X4677] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4677,X4676)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4677,c_Nat_OSuc(X4676)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_1335,plain,
! [X4832,X4833] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4833,X4832)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4833,c_Nat_OSuc(X4832)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_1336,plain,
! [X4699,X4700] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4700,X4699)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4700,c_Nat_OSuc(X4699)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_1337,plain,
! [X25,X26] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X25),X26),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_1338,plain,
! [X26,X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X26),X26),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_1339,plain,
! [X19] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X19),X19))
<=> X19 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(i_0_1340,plain,
! [X4990,X4991] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4991),X4990) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4990 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4991 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4990 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4991),X4990) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4991 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4991),X4990) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff])])]) ).
fof(i_0_1341,plain,
! [X33,X34] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X33)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X33)) = X34 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(i_0_1342,plain,
! [X21,X19,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
& ~ c_Orderings_Oord__class_Oless__eq(X10,X21,X19) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_1343,plain,
! [X5560] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X5560)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5560),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc]) ).
fof(i_0_1344,plain,
! [X5023,X5024] :
( ~ class_Power_Opower(X5024)
| ~ class_Rings_Osemiring__0(X5024)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5024),c_Groups_Ozero__class_Ozero(X5024)),c_Nat_OSuc(X5023)) = c_Groups_Ozero__class_Ozero(X5024) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).
fof(i_0_1345,plain,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> X19 = X21 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_1346,plain,
! [X4,X13,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X13,X4)
=> ~ c_Orderings_Oord__class_Oless(X10,X4,X13) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_1347,plain,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> ( c_Orderings_Oord__class_Oless(X10,X21,X19)
| X19 = X21 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_1348,plain,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> c_Orderings_Oord__class_Oless__eq(X10,X21,X19) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_1349,plain,
! [X9,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X9)
=> ~ c_Orderings_Oord__class_Oless(X10,X9,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_1350,plain,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
<=> c_Orderings_Oord__class_Oless(X10,X21,X19) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_1351,plain,
! [X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X9) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_1352,plain,
! [X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X9) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_1353,plain,
! [X13,X4,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X4,X13)
=> ~ c_Orderings_Oord__class_Oless(X10,X13,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_1354,plain,
! [X8,X9,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X9) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_1355,plain,
! [X4510,X4511] :
( c_Nat_OSuc(X4511) != c_Nat_OSuc(X4510)
| X4511 = X4510 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1356,plain,
! [X4508,X4509] :
( ( c_Nat_OSuc(X4509) != c_Nat_OSuc(X4508)
| X4509 = X4508 )
& ( X4509 != X4508
| c_Nat_OSuc(X4509) = c_Nat_OSuc(X4508) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1357,plain,
! [X13,X4] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13)
=> ( X4 != X13
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__neq__trans]) ).
fof(i_0_1358,plain,
! [X8,X9] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X9,X8)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X9) )
| X9 = X8 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).
fof(i_0_1359,plain,
! [X13,X4] :
( X4 != X13
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X13)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oneq__le__trans]) ).
fof(i_0_1360,plain,
! [X21,X19] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X21)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X19) )
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X21)
& X19 != X21 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le]) ).
fof(i_0_1361,plain,
! [X21,X19] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X21)
<=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X21)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X19) )
| X19 = X21 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less]) ).
fof(i_0_1362,plain,
! [X5362] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5362),
inference(variable_rename,[status(thm)],[fact_dvd__1__left]) ).
fof(i_0_1363,plain,
! [X4857] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4857),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4857,
inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).
fof(i_0_1364,plain,
! [X4502] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X4502)),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_1365,plain,
! [X4499] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4499,c_Nat_OSuc(X4499)),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_1366,plain,
! [X4795,X4797,X4798] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4795)
| X4795 = c_Nat_OSuc(esk16_1(X4795)) )
& ( X4797 != c_Nat_OSuc(X4798)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4797) ) ),
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_1367,plain,
! [X9,X8] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X9)
=> c_Nat__Transfer_Otsub(X9,X8) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X8) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X9)
=> c_Nat__Transfer_Otsub(X9,X8) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).
fof(i_0_1368,plain,
! [X21,X19,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X19,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X19,X21)
<=> X19 = X21 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_1369,plain,
! [X9,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero]) ).
fof(i_0_1370,plain,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X33),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_simplification,[status(thm)],[fact_not__real__of__nat__less__zero]) ).
fof(i_0_1371,plain,
! [X8,X9,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( X9 != X8
=> ( ~ c_Orderings_Oord__class_Oless(X10,X9,X8)
=> c_Orderings_Oord__class_Oless(X10,X8,X9) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_1372,plain,
! [X19,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X21,X19)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X19,X21)
<=> X19 = X21 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_1373,plain,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( X9 != X8
=> ( ~ c_Orderings_Oord__class_Oless(X10,X9,X8)
=> c_Orderings_Oord__class_Oless(X10,X8,X9) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_1374,plain,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X9,X8)
=> ( X9 != X8
=> c_Orderings_Oord__class_Oless(X10,X8,X9) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_1375,plain,
! [X9,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X8,X9)
=> c_Orderings_Oord__class_Oless(X10,X9,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_1376,plain,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X8,X9) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_1377,plain,
! [X8,X9,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X8,X9) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_1378,plain,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_1379,plain,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_1380,plain,
! [X4854] : c_Nat_OSuc(X4854) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4854),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1381,plain,
! [X8,X9] :
( X9 != X8
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X8)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X9) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_1382,plain,
! [X9,X10] :
( class_Orderings_Opreorder(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,X9,X9) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_1383,plain,
! [X4656] : c_Nat_OSuc(X4656) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1384,plain,
! [X4654] : c_Nat_OSuc(X4654) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1385,plain,
! [X4653] : c_Nat_OSuc(X4653) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1386,plain,
! [X4655] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X4655),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1387,plain,
! [X4652] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X4652),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1388,plain,
! [X4651] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X4651),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1389,plain,
! [X4507] : c_Nat_OSuc(X4507) != X4507,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1390,plain,
! [X4506] : X4506 != c_Nat_OSuc(X4506),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1391,plain,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_1392,plain,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_1393,plain,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_1394,plain,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X33),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_1395,plain,
! [X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X33),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_1396,plain,
! [X10] :
( class_Rings_Olinordered__idom(X10)
=> ~ c_Polynomial_Opos__poly(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) ),
inference(fof_simplification,[status(thm)],[fact_not__pos__poly__0]) ).
fof(i_0_1397,plain,
! [X21,X19] :
( ~ hBOOL(c_fequal(X19,X21))
| X19 = X21 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_1398,plain,
! [X5619,X5620,X5621,X5622,X5624] :
( ( c_Orderings_Oord__class_Oless__eq(X5621,X5620,esk36_4(X5619,X5620,X5621,X5622))
| ~ c_Orderings_Oord__class_Oless__eq(X5621,X5620,X5624)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5622,hAPP(X5619,X5624)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5622,hAPP(X5619,X5620))))
| ~ class_RealVector_Oreal__normed__vector(X5622)
| ~ class_Orderings_Oord(X5621) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5622,c_Groups_Ominus__class_Ominus(X5622,hAPP(X5619,X5620),hAPP(X5619,esk36_4(X5619,X5620,X5621,X5622)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(X5621,X5620,X5624)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5622,hAPP(X5619,X5624)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5622,hAPP(X5619,X5620))))
| ~ class_RealVector_Oreal__normed__vector(X5622)
| ~ class_Orderings_Oord(X5621) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemmaCauchy])])])])]) ).
fof(i_0_1399,plain,
! [X3151,X3152,X3153,X3154,X3155,X3156] :
( ~ class_Groups_Ozero(X3156)
| c_Polynomial_Opoly__rec(X3155,X3156,X3154,X3153,c_Polynomial_OpCons(X3156,X3152,X3151)) = hAPP(hAPP(hAPP(X3153,X3152),X3151),c_If(X3155,c_fequal(X3151,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3156))),X3154,c_Polynomial_Opoly__rec(X3155,X3156,X3154,X3153,X3151))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__rec_Osimps])]) ).
cnf(i_0_1400,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X3,X2))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1241]) ).
cnf(i_0_1401,plain,
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_1242]) ).
cnf(i_0_1402,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Nat_OSuc(c_Polynomial_Oorder(X1,X2,X3))),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1243]) ).
fof(i_0_1403,plain,
! [X3145,X3146,X3147,X3148,X3149,X3150] :
( ~ class_Groups_Ozero(X3150)
| hAPP(hAPP(hAPP(X3149,c_Groups_Ozero__class_Ozero(X3150)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3150))),X3148) != X3148
| c_Polynomial_Opoly__rec(X3147,X3150,X3148,X3149,c_Polynomial_OpCons(X3150,X3146,X3145)) = hAPP(hAPP(hAPP(X3149,X3146),X3145),c_Polynomial_Opoly__rec(X3147,X3150,X3148,X3149,X3145)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__rec__pCons])]) ).
fof(i_0_1404,plain,
! [X3077,X3078,X3079,X3080,X3081] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3079,X3080),X3078,X3077)
| c_Orderings_Oord__class_Oless__eq(X3080,hAPP(X3078,X3081),hAPP(X3077,X3081))
| ~ class_Orderings_Oord(X3080) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3080,hAPP(X3078,esk3_4(X3077,X3078,X3079,X3080)),hAPP(X3077,esk3_4(X3077,X3078,X3079,X3080)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3079,X3080),X3078,X3077)
| ~ class_Orderings_Oord(X3080) ) ),
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_1405,plain,
! [X3386,X3387,X3388,X3389,X3390] :
( ~ class_RealVector_Oreal__normed__algebra(X3390)
| c_Groups_Ominus__class_Ominus(X3390,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3390),X3389),X3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3390),X3387),X3386)) = c_Groups_Oplus__class_Oplus(X3390,c_Groups_Oplus__class_Oplus(X3390,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3390),c_Groups_Ominus__class_Ominus(X3390,X3389,X3387)),c_Groups_Ominus__class_Ominus(X3390,X3388,X3386)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3390),c_Groups_Ominus__class_Ominus(X3390,X3389,X3387)),X3386)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3390),X3387),c_Groups_Ominus__class_Ominus(X3390,X3388,X3386))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod])]) ).
fof(i_0_1406,plain,
! [X4482,X4483,X4484] :
( ~ class_Rings_Ocomm__ring__1(X4484)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4484)),c_Polynomial_OpCons(X4484,c_Groups_Ouminus__class_Ouminus(X4484,X4483),c_Polynomial_OpCons(X4484,c_Groups_Oone__class_Oone(X4484),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4484))))),c_Polynomial_Osynthetic__div(X4484,X4482,X4483)),c_Polynomial_OpCons(X4484,hAPP(c_Polynomial_Opoly(X4484,X4482),X4483),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4484)))) = X4482 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct_H])]) ).
fof(i_0_1407,plain,
! [X4443,X4444,X4445,X4446,X4447,X4448] :
( ( ~ c_Orderings_Oord__class_Oless(X4448,c_Groups_Oplus__class_Oplus(X4448,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4448),X4447),X4446),X4445),c_Groups_Oplus__class_Oplus(X4448,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4448),X4444),X4446),X4443))
| c_Orderings_Oord__class_Oless(X4448,c_Groups_Oplus__class_Oplus(X4448,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4448),c_Groups_Ominus__class_Ominus(X4448,X4447,X4444)),X4446),X4445),X4443)
| ~ class_Rings_Oordered__ring(X4448) )
& ( ~ c_Orderings_Oord__class_Oless(X4448,c_Groups_Oplus__class_Oplus(X4448,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4448),c_Groups_Ominus__class_Ominus(X4448,X4447,X4444)),X4446),X4445),X4443)
| c_Orderings_Oord__class_Oless(X4448,c_Groups_Oplus__class_Oplus(X4448,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4448),X4447),X4446),X4445),c_Groups_Oplus__class_Oplus(X4448,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4448),X4444),X4446),X4443))
| ~ class_Rings_Oordered__ring(X4448) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).
fof(i_0_1408,plain,
! [X3663,X3664,X3665,X3666,X3667,X3668] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3668,c_Groups_Oplus__class_Oplus(X3668,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3668),X3667),X3666),X3665),c_Groups_Oplus__class_Oplus(X3668,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3668),X3664),X3666),X3663))
| c_Orderings_Oord__class_Oless__eq(X3668,c_Groups_Oplus__class_Oplus(X3668,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3668),c_Groups_Ominus__class_Ominus(X3668,X3667,X3664)),X3666),X3665),X3663)
| ~ class_Rings_Oordered__ring(X3668) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3668,c_Groups_Oplus__class_Oplus(X3668,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3668),c_Groups_Ominus__class_Ominus(X3668,X3667,X3664)),X3666),X3665),X3663)
| c_Orderings_Oord__class_Oless__eq(X3668,c_Groups_Oplus__class_Oplus(X3668,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3668),X3667),X3666),X3665),c_Groups_Oplus__class_Oplus(X3668,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3668),X3664),X3666),X3663))
| ~ class_Rings_Oordered__ring(X3668) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).
fof(i_0_1409,plain,
! [X4437,X4438,X4439,X4440,X4441,X4442] :
( ( ~ c_Orderings_Oord__class_Oless(X4442,c_Groups_Oplus__class_Oplus(X4442,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4442),X4441),X4440),X4439),c_Groups_Oplus__class_Oplus(X4442,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4442),X4438),X4440),X4437))
| c_Orderings_Oord__class_Oless(X4442,X4439,c_Groups_Oplus__class_Oplus(X4442,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4442),c_Groups_Ominus__class_Ominus(X4442,X4438,X4441)),X4440),X4437))
| ~ class_Rings_Oordered__ring(X4442) )
& ( ~ c_Orderings_Oord__class_Oless(X4442,X4439,c_Groups_Oplus__class_Oplus(X4442,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4442),c_Groups_Ominus__class_Ominus(X4442,X4438,X4441)),X4440),X4437))
| c_Orderings_Oord__class_Oless(X4442,c_Groups_Oplus__class_Oplus(X4442,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4442),X4441),X4440),X4439),c_Groups_Oplus__class_Oplus(X4442,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4442),X4438),X4440),X4437))
| ~ class_Rings_Oordered__ring(X4442) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).
fof(i_0_1410,plain,
! [X3669,X3670,X3671,X3672,X3673,X3674] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3674,c_Groups_Oplus__class_Oplus(X3674,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3674),X3673),X3672),X3671),c_Groups_Oplus__class_Oplus(X3674,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3674),X3670),X3672),X3669))
| c_Orderings_Oord__class_Oless__eq(X3674,X3671,c_Groups_Oplus__class_Oplus(X3674,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3674),c_Groups_Ominus__class_Ominus(X3674,X3670,X3673)),X3672),X3669))
| ~ class_Rings_Oordered__ring(X3674) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3674,X3671,c_Groups_Oplus__class_Oplus(X3674,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3674),c_Groups_Ominus__class_Ominus(X3674,X3670,X3673)),X3672),X3669))
| c_Orderings_Oord__class_Oless__eq(X3674,c_Groups_Oplus__class_Oplus(X3674,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3674),X3673),X3672),X3671),c_Groups_Oplus__class_Oplus(X3674,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3674),X3670),X3672),X3669))
| ~ class_Rings_Oordered__ring(X3674) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).
fof(i_0_1411,plain,
! [X3921,X3922,X3923,X3924,X3925] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3924),X3923),X3922),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3925),X3923),X3921))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3924,X3925)),X3923),X3922),X3921)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3925,X3924) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3924,X3925)),X3923),X3922),X3921)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3924),X3923),X3922),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3925),X3923),X3921))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3925,X3924) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).
fof(i_0_1412,plain,
! [X3837,X3838,X3839,X3840,X3841] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3840),X3839),X3838),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3841),X3839),X3837))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3840,X3841)),X3839),X3838),X3837)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3841,X3840) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3840,X3841)),X3839),X3838),X3837)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3840),X3839),X3838),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3841),X3839),X3837))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3841,X3840) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).
fof(i_0_1413,plain,
! [X3926,X3927,X3928,X3929,X3930] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3930),X3928),X3927),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3929),X3928),X3926))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3927,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3929,X3930)),X3928),X3926))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3930,X3929) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3927,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3929,X3930)),X3928),X3926))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3930),X3928),X3927),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3929),X3928),X3926))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3930,X3929) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).
fof(i_0_1414,plain,
! [X3852,X3853,X3854,X3855,X3856] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3856),X3854),X3853),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3855),X3854),X3852))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3853,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3855,X3856)),X3854),X3852))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3856,X3855) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3853,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3855,X3856)),X3854),X3852))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3856),X3854),X3853),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3855),X3854),X3852))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3856,X3855) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).
fof(i_0_1415,plain,
! [X5344,X5345,X5346] :
( ~ class_Rings_Oidom(X5346)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5346),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5346)),c_Polynomial_OpCons(X5346,c_Groups_Ouminus__class_Ouminus(X5346,X5345),c_Polynomial_OpCons(X5346,c_Groups_Oone__class_Oone(X5346),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5346))))),c_Polynomial_Oorder(X5346,X5345,X5344)),X5344) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__1])]) ).
fof(i_0_1416,plain,
! [X5430,X5431] :
( X5431 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X5430 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X5431),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk21_2(X5430,X5431)),X5430)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduce__poly__simple])])]) ).
fof(i_0_1417,plain,
! [X3222,X3223,X3224,X3225,X3226] :
( ~ class_RealVector_Oreal__normed__vector(X3226)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3226,c_Groups_Ominus__class_Ominus(X3226,c_Groups_Oplus__class_Oplus(X3226,X3225,X3224),c_Groups_Oplus__class_Oplus(X3226,X3223,X3222))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3226,c_Groups_Ominus__class_Ominus(X3226,X3225,X3223)),c_RealVector_Onorm__class_Onorm(X3226,c_Groups_Ominus__class_Ominus(X3226,X3224,X3222)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__triangle__ineq])]) ).
fof(i_0_1418,plain,
! [X5522,X5523,X5524,X5526] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk25_3(X5522,X5523,X5524))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5524) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X5526,X5523)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X5526,X5523)),esk25_3(X5522,X5523,X5524))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X5522),X5526),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X5522),X5523))),X5524)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5524) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__cont])])])])]) ).
cnf(i_0_1419,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1244]) ).
fof(i_0_1420,plain,
! [X3842,X3843,X3844,X3845,X3846] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3846,X3845)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3845),X3844),X3843),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3846),X3844),X3842)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3845,X3846)),X3844),X3843),X3842) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).
fof(i_0_1421,plain,
! [X3857,X3858,X3859,X3860,X3861] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3861,X3860)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3861),X3859),X3858),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3860),X3859),X3857)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3858,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3860,X3861)),X3859),X3857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).
fof(i_0_1422,hypothesis,
! [X5795] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5795,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk38_1(X5795)))
| v_thesis____ )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),esk38_1(X5795))))
| v_thesis____ ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])])])]) ).
cnf(i_0_1423,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1245]) ).
cnf(i_0_1424,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1246]) ).
cnf(i_0_1425,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk35_2(X1,X2)))),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1247]) ).
fof(i_0_1426,plain,
! [X5356,X5357,X5358,X5359,X5360,X5361] :
( ( ~ c_Rings_Odvd__class_Odvd(X5359,X5358,c_Groups_Oplus__class_Oplus(X5359,X5360,X5356))
| c_Rings_Odvd__class_Odvd(X5359,X5358,c_Groups_Oplus__class_Oplus(X5359,c_Groups_Ominus__class_Ominus(X5359,X5360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5359),X5361),X5357)),X5356))
| ~ c_Rings_Odvd__class_Odvd(X5359,X5358,X5357)
| ~ class_Rings_Ocomm__ring(X5359)
| ~ class_Rings_Odvd(X5359) )
& ( ~ c_Rings_Odvd__class_Odvd(X5359,X5358,c_Groups_Oplus__class_Oplus(X5359,c_Groups_Ominus__class_Ominus(X5359,X5360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5359),X5361),X5357)),X5356))
| c_Rings_Odvd__class_Odvd(X5359,X5358,c_Groups_Oplus__class_Oplus(X5359,X5360,X5356))
| ~ c_Rings_Odvd__class_Odvd(X5359,X5358,X5357)
| ~ class_Rings_Ocomm__ring(X5359)
| ~ class_Rings_Odvd(X5359) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J])])])]) ).
fof(i_0_1427,plain,
! [X5350,X5351,X5352,X5353,X5354,X5355] :
( ( ~ c_Rings_Odvd__class_Odvd(X5353,X5352,c_Groups_Oplus__class_Oplus(X5353,X5354,X5350))
| c_Rings_Odvd__class_Odvd(X5353,X5352,c_Groups_Oplus__class_Oplus(X5353,c_Groups_Ominus__class_Ominus(X5353,X5354,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5353),X5355),X5351)),X5350))
| ~ c_Rings_Odvd__class_Odvd(X5353,X5352,X5351)
| ~ class_Rings_Ocomm__ring(X5353)
| ~ class_Rings_Odvd(X5353) )
& ( ~ c_Rings_Odvd__class_Odvd(X5353,X5352,c_Groups_Oplus__class_Oplus(X5353,c_Groups_Ominus__class_Ominus(X5353,X5354,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5353),X5355),X5351)),X5350))
| c_Rings_Odvd__class_Odvd(X5353,X5352,c_Groups_Oplus__class_Oplus(X5353,X5354,X5350))
| ~ c_Rings_Odvd__class_Odvd(X5353,X5352,X5351)
| ~ class_Rings_Ocomm__ring(X5353)
| ~ class_Rings_Odvd(X5353) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J])])])]) ).
fof(i_0_1428,plain,
! [X3164,X3165,X3166,X3167] :
( ~ class_Groups_Ozero(X3167)
| hAPP(hAPP(hAPP(X3166,c_Groups_Ozero__class_Ozero(X3167)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3167))),X3165) != X3165
| c_Polynomial_Opoly__rec(X3164,X3167,X3165,X3166,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3167))) = X3165 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__rec__0])]) ).
cnf(i_0_1429,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk31_2(X3,X2))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,esk30_3(X3,X2,X1))),X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1248]) ).
cnf(i_0_1430,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk27_2(X3,X2))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,esk26_3(X3,X2,X1))),X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1249]) ).
cnf(i_0_1431,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk33_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk32_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1248]) ).
cnf(i_0_1432,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk29_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk28_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1249]) ).
fof(i_0_1433,plain,
! [X5195,X5196,X5197,X5198,X5199,X5200] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5200),X5199),X5198) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5197),X5196),X5195)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5197),X5196),X5195),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5198,X5200)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5195)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5197)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5197,X5200)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5196,X5199) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).
fof(i_0_1434,plain,
! [X5184,X5185,X5186,X5187,X5188,X5189] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5189),X5188),X5187) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5186),X5185),X5184)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5186),X5185),X5184))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5184,X5186)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5187)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5186)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5186,X5189)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5188,X5185) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).
fof(i_0_1435,plain,
! [X5386,X5387,X5388,X5389,X5390] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5390,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5388,X5387))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5390,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5388,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5386),X5389)),X5387))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5390,X5389) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5390,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5388,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5386),X5389)),X5387))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5390,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5388,X5387))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5390,X5389) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__period])])]) ).
fof(i_0_1436,plain,
! [X5510,X5512,X5513] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk22_1(X5510))
| ~ class_RealVector_Oreal__normed__algebra(X5510) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5510,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5510),X5512),X5513)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5510,X5512)),c_RealVector_Onorm__class_Onorm(X5510,X5513))),esk22_1(X5510)))
| ~ class_RealVector_Oreal__normed__algebra(X5510) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Opos__bounded])])])])]) ).
fof(i_0_1437,plain,
! [X3907,X3909,X3910] :
( ~ class_RealVector_Oreal__normed__algebra(X3907)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3907),X3909),X3910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3907,X3909)),c_RealVector_Onorm__class_Onorm(X3907,X3910))),esk10_1(X3907))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Obounded])])])]) ).
fof(i_0_1438,plain,
! [X3895,X3897,X3898] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk7_1(X3895))
| ~ class_RealVector_Oreal__normed__algebra(X3895) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3895,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3895),X3897),X3898)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3895,X3897)),c_RealVector_Onorm__class_Onorm(X3895,X3898))),esk7_1(X3895)))
| ~ class_RealVector_Oreal__normed__algebra(X3895) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ononneg__bounded])])])])]) ).
cnf(i_0_1439,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_2(X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk32_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1248]) ).
cnf(i_0_1440,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk29_2(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk28_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1249]) ).
fof(i_0_1441,plain,
! [X5179,X5180,X5181,X5182,X5183] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5183),X5182),X5181),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5183),X5180),X5179))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5181)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5181,X5183)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5179,X5183)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5182,X5180) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).
fof(i_0_1442,plain,
! [X5190,X5191,X5192,X5193,X5194] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5194),X5193),X5192),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5194),X5191),X5190))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5190,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5194,X5190)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5194,X5192)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5191,X5193) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).
cnf(i_0_1443,plain,
( X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1250]) ).
cnf(i_0_1444,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Nat_OSuc(X3)))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1251]) ).
fof(i_0_1445,plain,
! [X3847,X3848,X3849,X3850,X3851] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3850),X3849),X3848) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3851),X3849),X3847)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3850,X3851)),X3849),X3848) = X3847
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3851,X3850) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3850,X3851)),X3849),X3848) != X3847
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3850),X3849),X3848) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3851),X3849),X3847)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3851,X3850) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).
fof(i_0_1446,plain,
! [X3862,X3863,X3864,X3865,X3866] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3866),X3864),X3863) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3865),X3864),X3862)
| X3863 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3865,X3866)),X3864),X3862)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3866,X3865) )
& ( X3863 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3865,X3866)),X3864),X3862)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3866),X3864),X3863) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3865),X3864),X3862)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3866,X3865) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).
fof(i_0_1447,plain,
! [X3689,X3690,X3691,X3692,X3693,X3694] :
( ( c_Groups_Oplus__class_Oplus(X3694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3694),X3693),X3692),X3691) != c_Groups_Oplus__class_Oplus(X3694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3694),X3690),X3692),X3689)
| c_Groups_Oplus__class_Oplus(X3694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3694),c_Groups_Ominus__class_Ominus(X3694,X3693,X3690)),X3692),X3691) = X3689
| ~ class_Rings_Oring(X3694) )
& ( c_Groups_Oplus__class_Oplus(X3694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3694),c_Groups_Ominus__class_Ominus(X3694,X3693,X3690)),X3692),X3691) != X3689
| c_Groups_Oplus__class_Oplus(X3694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3694),X3693),X3692),X3691) = c_Groups_Oplus__class_Oplus(X3694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3694),X3690),X3692),X3689)
| ~ class_Rings_Oring(X3694) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).
fof(i_0_1448,plain,
! [X3683,X3684,X3685,X3686,X3687,X3688] :
( ( c_Groups_Oplus__class_Oplus(X3688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3688),X3687),X3686),X3685) != c_Groups_Oplus__class_Oplus(X3688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3688),X3684),X3686),X3683)
| X3685 = c_Groups_Oplus__class_Oplus(X3688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3688),c_Groups_Ominus__class_Ominus(X3688,X3684,X3687)),X3686),X3683)
| ~ class_Rings_Oring(X3688) )
& ( X3685 != c_Groups_Oplus__class_Oplus(X3688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3688),c_Groups_Ominus__class_Ominus(X3688,X3684,X3687)),X3686),X3683)
| c_Groups_Oplus__class_Oplus(X3688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3688),X3687),X3686),X3685) = c_Groups_Oplus__class_Oplus(X3688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3688),X3684),X3686),X3683)
| ~ class_Rings_Oring(X3688) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).
cnf(i_0_1449,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1245]) ).
cnf(i_0_1450,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X3)),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1246]) ).
fof(i_0_1451,plain,
! [X2930,X2931,X2933] :
( v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,esk2_2(X2930,X2931),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2933))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2931,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X2930,v_cs____)),X2933))) ),
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_pCons_Ohyps])])])])]) ).
fof(i_0_1452,plain,
! [X5223] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5223) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X5223,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X5223,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X5223,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X5223,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unimodular__reduce__norm])]) ).
fof(i_0_1453,plain,
! [X3391,X3392,X3393,X3394,X3395] :
( ~ class_Rings_Oring(X3395)
| c_Groups_Ominus__class_Ominus(X3395,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3395),X3394),X3393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3395),X3392),X3391)) = c_Groups_Oplus__class_Oplus(X3395,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3395),X3394),c_Groups_Ominus__class_Ominus(X3395,X3393,X3391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3395),c_Groups_Ominus__class_Ominus(X3395,X3394,X3392)),X3391)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__diff__mult])]) ).
fof(i_0_1454,plain,
! [X5592,X5593] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5593)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5592)),X5593),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5593,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X5592)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LIMSEQ__inverse__realpow__zero__lemma])]) ).
cnf(i_0_1455,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))),X4)
| ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1252]) ).
fof(i_0_1456,plain,
! [X3775,X3776,X3777,X3778,X3779] :
( ~ class_Rings_Osemiring(X3779)
| c_Groups_Oplus__class_Oplus(X3779,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3779),X3778),X3777),c_Groups_Oplus__class_Oplus(X3779,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3779),X3776),X3777),X3775)) = c_Groups_Oplus__class_Oplus(X3779,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3779),c_Groups_Oplus__class_Oplus(X3779,X3778,X3776)),X3777),X3775) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_1457,plain,
! [X4210,X4211,X4212,X4213,X4214,X4215] :
( ~ class_Rings_Olinordered__semiring__1__strict(X4215)
| ~ c_Orderings_Oord__class_Oless(X4215,X4214,X4213)
| ~ c_Orderings_Oord__class_Oless(X4215,X4212,X4213)
| ~ c_Orderings_Oord__class_Oless__eq(X4215,c_Groups_Ozero__class_Ozero(X4215),X4211)
| ~ c_Orderings_Oord__class_Oless__eq(X4215,c_Groups_Ozero__class_Ozero(X4215),X4210)
| c_Groups_Oplus__class_Oplus(X4215,X4211,X4210) != c_Groups_Oone__class_Oone(X4215)
| c_Orderings_Oord__class_Oless(X4215,c_Groups_Oplus__class_Oplus(X4215,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4215),X4211),X4214),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4215),X4210),X4212)),X4213) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).
fof(i_0_1458,plain,
! [X4476,X4477,X4478,X4479,X4480,X4481] :
( ~ class_Rings_Olinordered__semiring__1(X4481)
| ~ c_Orderings_Oord__class_Oless__eq(X4481,X4480,X4479)
| ~ c_Orderings_Oord__class_Oless__eq(X4481,X4478,X4479)
| ~ c_Orderings_Oord__class_Oless__eq(X4481,c_Groups_Ozero__class_Ozero(X4481),X4477)
| ~ c_Orderings_Oord__class_Oless__eq(X4481,c_Groups_Ozero__class_Ozero(X4481),X4476)
| c_Groups_Oplus__class_Oplus(X4481,X4477,X4476) != c_Groups_Oone__class_Oone(X4481)
| c_Orderings_Oord__class_Oless__eq(X4481,c_Groups_Oplus__class_Oplus(X4481,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4481),X4477),X4480),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4481),X4476),X4478)),X4479) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).
fof(i_0_1459,plain,
! [X5423,X5424,X5425,X5426,X5428] :
( ( c_Rings_Odvd__class_Odvd(X5425,X5423,c_Groups_Oplus__class_Oplus(X5425,esk19_3(X5423,X5424,X5425),c_Groups_Ozero__class_Ozero(X5425)))
| ~ hBOOL(hAPP(X5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5425),X5423),X5426)))
| ~ class_Rings_Odvd(X5425)
| ~ class_Rings_Osemiring__0(X5425) )
& ( hBOOL(hAPP(X5424,esk19_3(X5423,X5424,X5425)))
| ~ hBOOL(hAPP(X5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5425),X5423),X5426)))
| ~ class_Rings_Odvd(X5425)
| ~ class_Rings_Osemiring__0(X5425) )
& ( ~ c_Rings_Odvd__class_Odvd(X5425,X5423,c_Groups_Oplus__class_Oplus(X5425,X5428,c_Groups_Ozero__class_Ozero(X5425)))
| ~ hBOOL(hAPP(X5424,X5428))
| hBOOL(hAPP(X5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5425),X5423),esk20_3(X5423,X5424,X5425))))
| ~ class_Rings_Odvd(X5425)
| ~ class_Rings_Osemiring__0(X5425) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex])])])])]) ).
fof(i_0_1460,plain,
! [X3880,X3881,X3882,X3883] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3883),X3882),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3881),X3882),X3880)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3883,X3881)),X3882),X3880),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(i_0_1461,plain,
! [X4428,X4429,X4430] :
( ( ~ c_Orderings_Oord__class_Oless(X4430,c_Groups_Ozero__class_Ozero(X4430),c_Groups_Oplus__class_Oplus(X4430,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4430),X4429),X4429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4430),X4428),X4428)))
| X4429 != c_Groups_Ozero__class_Ozero(X4430)
| X4428 != c_Groups_Ozero__class_Ozero(X4430)
| ~ class_Rings_Olinordered__ring__strict(X4430) )
& ( X4429 = c_Groups_Ozero__class_Ozero(X4430)
| c_Orderings_Oord__class_Oless(X4430,c_Groups_Ozero__class_Ozero(X4430),c_Groups_Oplus__class_Oplus(X4430,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4430),X4429),X4429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4430),X4428),X4428)))
| ~ class_Rings_Olinordered__ring__strict(X4430) )
& ( X4428 = c_Groups_Ozero__class_Ozero(X4430)
| c_Orderings_Oord__class_Oless(X4430,c_Groups_Ozero__class_Ozero(X4430),c_Groups_Oplus__class_Oplus(X4430,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4430),X4429),X4429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4430),X4428),X4428)))
| ~ class_Rings_Olinordered__ring__strict(X4430) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).
fof(i_0_1462,plain,
! [X3357,X3358,X3359,X3360,X3361] :
( ~ class_Rings_Ocomm__semiring__1(X3361)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3361),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3361),X3360),X3359)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3361),X3358),X3357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3361),X3358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3361),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3361),X3360),X3359)),X3357)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).
fof(i_0_1463,plain,
! [X3675,X3676,X3677] :
( ( X3676 = c_Groups_Ozero__class_Ozero(X3677)
| ~ c_Orderings_Oord__class_Oless__eq(X3677,c_Groups_Oplus__class_Oplus(X3677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3677),X3676),X3676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3677),X3675),X3675)),c_Groups_Ozero__class_Ozero(X3677))
| ~ class_Rings_Olinordered__ring__strict(X3677) )
& ( X3675 = c_Groups_Ozero__class_Ozero(X3677)
| ~ c_Orderings_Oord__class_Oless__eq(X3677,c_Groups_Oplus__class_Oplus(X3677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3677),X3676),X3676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3677),X3675),X3675)),c_Groups_Ozero__class_Ozero(X3677))
| ~ class_Rings_Olinordered__ring__strict(X3677) )
& ( X3676 != c_Groups_Ozero__class_Ozero(X3677)
| X3675 != c_Groups_Ozero__class_Ozero(X3677)
| c_Orderings_Oord__class_Oless__eq(X3677,c_Groups_Oplus__class_Oplus(X3677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3677),X3676),X3676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3677),X3675),X3675)),c_Groups_Ozero__class_Ozero(X3677))
| ~ class_Rings_Olinordered__ring__strict(X3677) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).
fof(i_0_1464,plain,
! [X4425,X4426,X4427] :
( ~ class_Rings_Olinordered__ring(X4427)
| ~ c_Orderings_Oord__class_Oless(X4427,c_Groups_Oplus__class_Oplus(X4427,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4427),X4426),X4426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4427),X4425),X4425)),c_Groups_Ozero__class_Ozero(X4427)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1253])]) ).
cnf(i_0_1465,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Nat_OSuc(X5)) = hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_1254]) ).
fof(i_0_1466,plain,
! [X3607,X3608,X3609,X3610] :
( ~ class_Rings_Ocomm__semiring__0(X3610)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3610)),c_Polynomial_OpCons(X3610,X3609,X3608)),X3607) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3610),c_Polynomial_Osmult(X3610,X3609,X3607),c_Polynomial_OpCons(X3610,c_Groups_Ozero__class_Ozero(X3610),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3610)),X3608),X3607))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__left])]) ).
fof(i_0_1467,plain,
! [X5341,X5342,X5343] :
( ( hAPP(c_Polynomial_Opoly(X5343,X5342),X5341) != c_Groups_Ozero__class_Ozero(X5343)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5343),c_Polynomial_OpCons(X5343,c_Groups_Ouminus__class_Ouminus(X5343,X5341),c_Polynomial_OpCons(X5343,c_Groups_Oone__class_Oone(X5343),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5343)))),X5342)
| ~ class_Rings_Oidom(X5343) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5343),c_Polynomial_OpCons(X5343,c_Groups_Ouminus__class_Ouminus(X5343,X5341),c_Polynomial_OpCons(X5343,c_Groups_Oone__class_Oone(X5343),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5343)))),X5342)
| hAPP(c_Polynomial_Opoly(X5343,X5342),X5341) = c_Groups_Ozero__class_Ozero(X5343)
| ~ class_Rings_Oidom(X5343) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__0__iff__dvd])])]) ).
fof(i_0_1468,plain,
! [X3227,X3228,X3229,X3230] :
( ~ class_Rings_Ocomm__semiring__0(X3230)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3230,c_Polynomial_OpCons(X3230,X3229,X3228),X3227) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3230),c_Polynomial_Osmult(X3230,X3227,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3230,X3228,X3227)),c_Polynomial_OpCons(X3230,X3229,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3230,X3228,X3227))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__pCons])]) ).
fof(i_0_1469,plain,
! [X4492,X4493,X4494] :
( ~ class_Groups_Omonoid__mult(X4494)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4493)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4494),hAPP(hAPP(c_Power_Opower__class_Opower(X4494),X4492),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4493,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X4492) = hAPP(hAPP(c_Power_Opower__class_Opower(X4494),X4492),X4493) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__minus__mult])]) ).
cnf(i_0_1470,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1255]) ).
fof(i_0_1471,plain,
! [X5338,X5339,X5340] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5340),c_Polynomial_OpCons(X5340,X5339,c_Polynomial_OpCons(X5340,c_Groups_Oone__class_Oone(X5340),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5340)))),X5338)
| hAPP(c_Polynomial_Opoly(X5340,X5338),c_Groups_Ouminus__class_Ouminus(X5340,X5339)) = c_Groups_Ozero__class_Ozero(X5340)
| ~ class_Rings_Oidom(X5340) )
& ( hAPP(c_Polynomial_Opoly(X5340,X5338),c_Groups_Ouminus__class_Ouminus(X5340,X5339)) != c_Groups_Ozero__class_Ozero(X5340)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5340),c_Polynomial_OpCons(X5340,X5339,c_Polynomial_OpCons(X5340,c_Groups_Oone__class_Oone(X5340),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5340)))),X5338)
| ~ class_Rings_Oidom(X5340) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__iff__poly__eq__0])])]) ).
fof(i_0_1472,plain,
! [X3569,X3570,X3571,X3572,X3573] :
( ( X3572 = X3571
| X3570 = X3569
| c_Groups_Oplus__class_Oplus(X3573,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3572),X3570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3571),X3569)) != c_Groups_Oplus__class_Oplus(X3573,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3572),X3569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3571),X3570))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3573) )
& ( X3572 != X3571
| c_Groups_Oplus__class_Oplus(X3573,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3572),X3570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3571),X3569)) = c_Groups_Oplus__class_Oplus(X3573,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3572),X3569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3571),X3570))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3573) )
& ( X3570 != X3569
| c_Groups_Oplus__class_Oplus(X3573,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3572),X3570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3571),X3569)) = c_Groups_Oplus__class_Oplus(X3573,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3572),X3569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3573),X3571),X3570))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3573) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_1473,plain,
! [X3556,X3557,X3558,X3559,X3560] :
( ( c_Groups_Oplus__class_Oplus(X3560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3559),X3558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3557),X3556)) != c_Groups_Oplus__class_Oplus(X3560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3559),X3556),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3557),X3558))
| X3559 = X3557
| X3558 = X3556
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3560) )
& ( X3559 != X3557
| c_Groups_Oplus__class_Oplus(X3560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3559),X3558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3557),X3556)) = c_Groups_Oplus__class_Oplus(X3560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3559),X3556),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3557),X3558))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3560) )
& ( X3558 != X3556
| c_Groups_Oplus__class_Oplus(X3560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3559),X3558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3557),X3556)) = c_Groups_Oplus__class_Oplus(X3560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3559),X3556),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3557),X3558))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3560) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
cnf(i_0_1474,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1250]) ).
fof(i_0_1475,plain,
! [X5671,X5672,X5673,X5674,X5675] :
( ~ class_Divides_Osemiring__div(X5675)
| ~ c_Rings_Odvd__class_Odvd(X5675,X5674,X5673)
| ~ c_Rings_Odvd__class_Odvd(X5675,X5672,X5671)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5675),c_Divides_Odiv__class_Odiv(X5675,X5673,X5674)),c_Divides_Odiv__class_Odiv(X5675,X5671,X5672)) = c_Divides_Odiv__class_Odiv(X5675,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5675),X5673),X5671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5675),X5674),X5672)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__div__if__dvd])]) ).
cnf(i_0_1476,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1256]) ).
cnf(i_0_1477,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1257]) ).
fof(i_0_1478,plain,
! [X3603,X3604,X3605,X3606] :
( ~ class_Rings_Ocomm__semiring__0(X3606)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3606)),X3605),c_Polynomial_OpCons(X3606,X3604,X3603)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3606),c_Polynomial_Osmult(X3606,X3604,X3605),c_Polynomial_OpCons(X3606,c_Groups_Ozero__class_Ozero(X3606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3606)),X3605),X3603))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__right])]) ).
fof(i_0_1479,plain,
! [X5062,X5063,X5064] :
( ~ class_Rings_Oring__1(X5064)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5064),c_Groups_Ouminus__class_Ouminus(X5064,X5063)),X5062) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5064),hAPP(hAPP(c_Power_Opower__class_Opower(X5064),c_Groups_Ouminus__class_Ouminus(X5064,c_Groups_Oone__class_Oone(X5064))),X5062)),hAPP(hAPP(c_Power_Opower__class_Opower(X5064),X5063),X5062)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).
fof(i_0_1480,plain,
! [X5176,X5177,X5178] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5178),X5177),X5176),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5176)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5178)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5177,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__neg__lemma])]) ).
fof(i_0_1481,plain,
! [X5173,X5174,X5175] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5175),X5174),X5173))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5173,X5175)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5175)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).
fof(i_0_1482,plain,
! [X3867,X3868,X3869,X3870] :
( ~ class_Rings_Ocomm__semiring__0(X3870)
| c_Polynomial_Opcompose(X3870,c_Polynomial_OpCons(X3870,X3869,X3868),X3867) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3870),c_Polynomial_OpCons(X3870,X3869,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3870))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3870)),X3867),c_Polynomial_Opcompose(X3870,X3868,X3867))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__pCons])]) ).
fof(i_0_1483,plain,
! [X3352,X3353,X3354,X3355,X3356] :
( ~ class_Rings_Ocomm__semiring__1(X3356)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3356),X3355),X3354)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3356),X3353),X3352)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3356),X3355),X3353)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3356),X3354),X3352)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).
fof(i_0_1484,plain,
! [X3362,X3363,X3364,X3365,X3366] :
( ~ class_Rings_Ocomm__semiring__1(X3366)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3366),X3365),X3364)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3366),X3363),X3362)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3366),X3365),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3366),X3364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3366),X3363),X3362))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).
cnf(i_0_1485,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1258]) ).
cnf(i_0_1486,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1259]) ).
cnf(i_0_1487,plain,
( X2 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Nat_OSuc(X3))
| ~ 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),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1260]) ).
cnf(i_0_1488,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(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)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1261]) ).
fof(i_0_1489,plain,
! [X3681,X3682] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3682,X3681)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3682)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3681)),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__ineq2]) ).
fof(i_0_1490,plain,
! [X3083,X3084] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3084),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3084,X3083)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3083))),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__sub]) ).
cnf(i_0_1491,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_1262]) ).
fof(i_0_1492,plain,
! [X3599,X3600,X3601,X3602] :
( ~ class_Rings_Ocomm__semiring__0(X3602)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3602)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3602),X3601,X3600)),X3599) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3602)),X3601),X3599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3602)),X3600),X3599)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__add__left])]) ).
fof(i_0_1493,plain,
! [X4468,X4469,X4470,X4471,X4472,X4473,X4474] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4469,X4468)
| hBOOL(hAPP(X4470,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4470,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4469,X4468))) )
& ( X4469 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4468,X4471)
| hBOOL(hAPP(X4470,X4471))
| ~ hBOOL(hAPP(X4470,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4469,X4468))) )
& ( X4473 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4472,esk14_3(X4472,X4473,X4474))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4473,X4472)
| hBOOL(hAPP(X4474,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4473,X4472))) )
& ( ~ hBOOL(hAPP(X4474,esk14_3(X4472,X4473,X4474)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4473,X4472)
| hBOOL(hAPP(X4474,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4473,X4472))) )
& ( X4473 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4472,esk14_3(X4472,X4473,X4474))
| ~ hBOOL(hAPP(X4474,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4474,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4473,X4472))) )
& ( ~ hBOOL(hAPP(X4474,esk14_3(X4472,X4473,X4474)))
| ~ hBOOL(hAPP(X4474,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4474,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4473,X4472))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__split])])])])])]) ).
fof(i_0_1494,plain,
! [X4460,X4461,X4462,X4463,X4464,X4465,X4466] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4461,X4460)
| hBOOL(hAPP(X4462,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4462,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4461,X4460))) )
& ( X4461 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4460,X4463)
| hBOOL(hAPP(X4462,X4463))
| ~ hBOOL(hAPP(X4462,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4461,X4460))) )
& ( X4465 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4464,esk13_3(X4464,X4465,X4466))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4465,X4464)
| hBOOL(hAPP(X4466,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4465,X4464))) )
& ( ~ hBOOL(hAPP(X4466,esk13_3(X4464,X4465,X4466)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4465,X4464)
| hBOOL(hAPP(X4466,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4465,X4464))) )
& ( X4465 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4464,esk13_3(X4464,X4465,X4466))
| ~ hBOOL(hAPP(X4466,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4466,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4465,X4464))) )
& ( ~ hBOOL(hAPP(X4466,esk13_3(X4464,X4465,X4466)))
| ~ hBOOL(hAPP(X4466,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4466,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4465,X4464))) ) ),
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_1263])])])])])]) ).
cnf(i_0_1495,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1264]) ).
cnf(i_0_1496,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1265]) ).
fof(i_0_1497,plain,
! [X3266,X3267,X3268,X3269,X3270] :
( ~ class_Rings_Ocomm__semiring__0(X3270)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3270)),c_Polynomial_Omonom(X3270,X3269,X3268)),c_Polynomial_Omonom(X3270,X3267,X3266)) = c_Polynomial_Omonom(X3270,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3270),X3269),X3267),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3268,X3266)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__monom])]) ).
fof(i_0_1498,plain,
! [X5081,X5082,X5083] :
( ~ class_Rings_Olinordered__semidom(X5083)
| ~ c_Orderings_Oord__class_Oless(X5083,c_Groups_Ozero__class_Ozero(X5083),X5082)
| ~ c_Orderings_Oord__class_Oless(X5083,X5082,c_Groups_Oone__class_Oone(X5083))
| c_Orderings_Oord__class_Oless(X5083,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5083),X5082),hAPP(hAPP(c_Power_Opower__class_Opower(X5083),X5082),X5081)),hAPP(hAPP(c_Power_Opower__class_Opower(X5083),X5082),X5081)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
fof(i_0_1499,plain,
! [X5667,X5668,X5669,X5670] :
( ( ~ c_Rings_Odvd__class_Odvd(X5670,c_Divides_Odiv__class_Odiv(X5670,X5668,X5669),c_Divides_Odiv__class_Odiv(X5670,X5667,X5669))
| c_Rings_Odvd__class_Odvd(X5670,X5668,X5667)
| ~ c_Rings_Odvd__class_Odvd(X5670,X5669,X5667)
| ~ c_Rings_Odvd__class_Odvd(X5670,X5669,X5668)
| ~ class_Divides_Osemiring__div(X5670) )
& ( ~ c_Rings_Odvd__class_Odvd(X5670,X5668,X5667)
| c_Rings_Odvd__class_Odvd(X5670,c_Divides_Odiv__class_Odiv(X5670,X5668,X5669),c_Divides_Odiv__class_Odiv(X5670,X5667,X5669))
| ~ c_Rings_Odvd__class_Odvd(X5670,X5669,X5667)
| ~ c_Rings_Odvd__class_Odvd(X5670,X5669,X5668)
| ~ class_Divides_Osemiring__div(X5670) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__dvd__div])])]) ).
fof(i_0_1500,plain,
! [X5129] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5129),X5129),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5129,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5129,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5129),X5129),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__less__0])]) ).
fof(i_0_1501,plain,
! [X4921,X4922,X4923,X4924,X4925] :
( ~ class_RealVector_Oreal__normed__vector(X4925)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4925,X4924),X4923)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4925,X4922),X4921)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4925,c_Groups_Oplus__class_Oplus(X4925,X4924,X4922)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4923,X4921)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__add__less])]) ).
cnf(i_0_1502,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Nat_OSuc(X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1266]) ).
fof(i_0_1503,plain,
! [X3484,X3485,X3486,X3487] :
( ~ class_Rings_Ocomm__semiring__0(X3487)
| hAPP(c_Polynomial_Opoly(X3487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3487)),X3486),X3485)),X3484) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3487),hAPP(c_Polynomial_Opoly(X3487,X3486),X3484)),hAPP(c_Polynomial_Opoly(X3487,X3485),X3484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])]) ).
fof(i_0_1504,plain,
! [X3919,X3920] :
( ( X3920 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3920),X3919) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3920 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3920),X3919) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3919,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3920,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3919)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).
fof(i_0_1505,plain,
! [X4348,X4349,X4350] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4349,X4350),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4348,X4350))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4349,X4348)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4350,X4348)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4350,X4349) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4349,X4348)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4349,X4350),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4348,X4350))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4350,X4348)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4350,X4349) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).
fof(i_0_1506,plain,
! [X3340,X3341,X3342] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3341,X3342),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3340,X3342))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3341,X3340)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3342,X3340)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3342,X3341) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3341,X3340)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3341,X3342),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3340,X3342))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3342,X3340)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3342,X3341) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).
fof(i_0_1507,plain,
! [X4361,X4362,X4363,X4364,X4365] :
( ~ class_Rings_Olinordered__semiring__strict(X4365)
| ~ c_Orderings_Oord__class_Oless(X4365,X4364,X4363)
| ~ c_Orderings_Oord__class_Oless(X4365,X4362,X4361)
| ~ c_Orderings_Oord__class_Oless(X4365,c_Groups_Ozero__class_Ozero(X4365),X4363)
| ~ c_Orderings_Oord__class_Oless__eq(X4365,c_Groups_Ozero__class_Ozero(X4365),X4362)
| c_Orderings_Oord__class_Oless(X4365,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4365),X4364),X4362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4365),X4363),X4361)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).
fof(i_0_1508,plain,
! [X4366,X4367,X4368,X4369,X4370] :
( ~ class_Rings_Olinordered__semiring__strict(X4370)
| ~ c_Orderings_Oord__class_Oless(X4370,X4369,X4368)
| ~ c_Orderings_Oord__class_Oless(X4370,X4367,X4366)
| ~ c_Orderings_Oord__class_Oless__eq(X4370,c_Groups_Ozero__class_Ozero(X4370),X4369)
| ~ c_Orderings_Oord__class_Oless__eq(X4370,c_Groups_Ozero__class_Ozero(X4370),X4367)
| c_Orderings_Oord__class_Oless(X4370,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4370),X4369),X4367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4370),X4368),X4366)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).
fof(i_0_1509,plain,
! [X4376,X4377,X4378,X4379,X4380] :
( ~ class_Rings_Olinordered__semiring__strict(X4380)
| ~ c_Orderings_Oord__class_Oless__eq(X4380,X4379,X4378)
| ~ c_Orderings_Oord__class_Oless(X4380,X4377,X4376)
| ~ c_Orderings_Oord__class_Oless(X4380,c_Groups_Ozero__class_Ozero(X4380),X4379)
| ~ c_Orderings_Oord__class_Oless__eq(X4380,c_Groups_Ozero__class_Ozero(X4380),X4377)
| c_Orderings_Oord__class_Oless(X4380,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4378),X4376)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).
fof(i_0_1510,plain,
! [X4371,X4372,X4373,X4374,X4375] :
( ~ class_Rings_Olinordered__semiring__strict(X4375)
| ~ c_Orderings_Oord__class_Oless(X4375,X4374,X4373)
| ~ c_Orderings_Oord__class_Oless__eq(X4375,X4372,X4371)
| ~ c_Orderings_Oord__class_Oless__eq(X4375,c_Groups_Ozero__class_Ozero(X4375),X4374)
| ~ c_Orderings_Oord__class_Oless(X4375,c_Groups_Ozero__class_Ozero(X4375),X4372)
| c_Orderings_Oord__class_Oless(X4375,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4375),X4374),X4372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4375),X4373),X4371)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).
fof(i_0_1511,plain,
! [X3791,X3792,X3793,X3794,X3795] :
( ~ class_Rings_Oordered__semiring(X3795)
| ~ c_Orderings_Oord__class_Oless__eq(X3795,X3794,X3793)
| ~ c_Orderings_Oord__class_Oless__eq(X3795,X3792,X3791)
| ~ c_Orderings_Oord__class_Oless__eq(X3795,c_Groups_Ozero__class_Ozero(X3795),X3794)
| ~ c_Orderings_Oord__class_Oless__eq(X3795,c_Groups_Ozero__class_Ozero(X3795),X3792)
| c_Orderings_Oord__class_Oless__eq(X3795,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3795),X3794),X3792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3795),X3793),X3791)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).
fof(i_0_1512,plain,
! [X3786,X3787,X3788,X3789,X3790] :
( ~ class_Rings_Oordered__semiring(X3790)
| ~ c_Orderings_Oord__class_Oless__eq(X3790,X3789,X3788)
| ~ c_Orderings_Oord__class_Oless__eq(X3790,X3787,X3786)
| ~ c_Orderings_Oord__class_Oless__eq(X3790,c_Groups_Ozero__class_Ozero(X3790),X3788)
| ~ c_Orderings_Oord__class_Oless__eq(X3790,c_Groups_Ozero__class_Ozero(X3790),X3787)
| c_Orderings_Oord__class_Oless__eq(X3790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3790),X3789),X3787),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3790),X3788),X3786)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).
fof(i_0_1513,plain,
! [X4910,X4911,X4912,X4913,X4914] :
( ~ class_RealVector_Oreal__normed__algebra(X4914)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4914,X4913),X4912)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4914,X4911),X4910)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4914,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4914),X4913),X4911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4912),X4910)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__less])]) ).
fof(i_0_1514,plain,
! [X3212,X3213,X3214] :
( ~ class_Rings_Ocomm__semiring__0(X3214)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3214),X3213,c_Polynomial_Osmult(X3214,X3212,c_Polynomial_Osynthetic__div(X3214,X3213,X3212))) = c_Polynomial_OpCons(X3214,hAPP(c_Polynomial_Opoly(X3214,X3213),X3212),c_Polynomial_Osynthetic__div(X3214,X3213,X3212)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct])]) ).
fof(i_0_1515,plain,
! [X4983,X4984,X4985,X4986] :
( ~ class_Groups_Ocomm__monoid__mult(X4986)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4986),X4985),X4984)),X4983) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4986),hAPP(hAPP(c_Power_Opower__class_Opower(X4986),X4985),X4983)),hAPP(hAPP(c_Power_Opower__class_Opower(X4986),X4984),X4983)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_1516,plain,
! [X4623,X4624,X4625,X4626] :
( ~ class_Rings_Ocomm__semiring__1(X4626)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4626),X4625),X4624)),X4623) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4626),hAPP(hAPP(c_Power_Opower__class_Opower(X4626),X4625),X4623)),hAPP(hAPP(c_Power_Opower__class_Opower(X4626),X4624),X4623)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_1517,plain,
! [X5692,X5693,X5694,X5695] :
( ~ class_Divides_Osemiring__div(X5695)
| ~ c_Rings_Odvd__class_Odvd(X5695,X5694,X5693)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5695),c_Divides_Odiv__class_Odiv(X5695,X5693,X5694)),X5692) = c_Divides_Odiv__class_Odiv(X5695,hAPP(hAPP(c_Power_Opower__class_Opower(X5695),X5693),X5692),hAPP(hAPP(c_Power_Opower__class_Opower(X5695),X5694),X5692)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__power])]) ).
fof(i_0_1518,plain,
! [X3157,X3158,X3160] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3160),X3158)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3157),esk4_2(X3157,X3158))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3157),X3160))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__minimum__modulus__disc])])]) ).
fof(i_0_1519,plain,
! [X5663,X5664,X5665,X5666] :
( ~ class_Divides_Osemiring__div(X5666)
| ~ c_Rings_Odvd__class_Odvd(X5666,X5665,X5664)
| ~ c_Rings_Odvd__class_Odvd(X5666,X5665,X5663)
| c_Divides_Odiv__class_Odiv(X5666,c_Groups_Oplus__class_Oplus(X5666,X5664,X5663),X5665) = c_Groups_Oplus__class_Oplus(X5666,c_Divides_Odiv__class_Odiv(X5666,X5664,X5665),c_Divides_Odiv__class_Odiv(X5666,X5663,X5665)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add])]) ).
fof(i_0_1520,plain,
! [X3678,X3679,X3680] :
( ~ class_Rings_Olinordered__ring(X3680)
| c_Orderings_Oord__class_Oless__eq(X3680,c_Groups_Ozero__class_Ozero(X3680),c_Groups_Oplus__class_Oplus(X3680,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3680),X3679),X3679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3680),X3678),X3678))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).
fof(i_0_1521,plain,
! [X5394,X5395,X5396] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5396,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5395,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5396),X5394)))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5396,X5395) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5396,X5395)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5396,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5395,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5396),X5394))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__reduce])]) ).
cnf(i_0_1522,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1267]) ).
fof(i_0_1523,plain,
! [X4449,X4450] :
( ~ class_Rings_Oring__1(X4450)
| c_Groups_Ominus__class_Ominus(X4450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4450),X4449),X4449),c_Groups_Oone__class_Oone(X4450)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4450),c_Groups_Oplus__class_Oplus(X4450,X4449,c_Groups_Oone__class_Oone(X4450))),c_Groups_Ominus__class_Ominus(X4450,X4449,c_Groups_Oone__class_Oone(X4450))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored])]) ).
cnf(i_0_1524,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1257]) ).
cnf(i_0_1525,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1257]) ).
cnf(i_0_1526,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1268]) ).
fof(i_0_1527,plain,
! [X3235,X3236,X3237,X3238] :
( ~ class_Rings_Ocomm__semiring__0(X3238)
| hAPP(c_Polynomial_Opoly(X3238,c_Polynomial_OpCons(X3238,X3237,X3236)),X3235) = c_Groups_Oplus__class_Oplus(X3238,X3237,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3238),X3235),hAPP(c_Polynomial_Opoly(X3238,X3236),X3235))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])]) ).
fof(i_0_1528,plain,
! [X5054,X5055,X5056] :
( ~ class_Rings_Olinordered__semidom(X5056)
| ~ c_Orderings_Oord__class_Oless(X5056,c_Groups_Oone__class_Oone(X5056),X5055)
| c_Orderings_Oord__class_Oless(X5056,hAPP(hAPP(c_Power_Opower__class_Opower(X5056),X5055),X5054),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5056),X5055),hAPP(hAPP(c_Power_Opower__class_Opower(X5056),X5055),X5054))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
fof(i_0_1529,plain,
! [X4381,X4382,X4383,X4384] :
( ~ class_Rings_Olinordered__semiring(X4384)
| ~ c_Orderings_Oord__class_Oless(X4384,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4384),X4383),X4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4384),X4381),X4382))
| ~ c_Orderings_Oord__class_Oless__eq(X4384,c_Groups_Ozero__class_Ozero(X4384),X4382)
| c_Orderings_Oord__class_Oless(X4384,X4383,X4381) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).
fof(i_0_1530,plain,
! [X4385,X4386,X4387,X4388] :
( ~ class_Rings_Olinordered__semiring__strict(X4388)
| ~ c_Orderings_Oord__class_Oless(X4388,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4388),X4387),X4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4388),X4385),X4386))
| ~ c_Orderings_Oord__class_Oless__eq(X4388,c_Groups_Ozero__class_Ozero(X4388),X4386)
| c_Orderings_Oord__class_Oless(X4388,X4387,X4385) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).
fof(i_0_1531,plain,
! [X5039,X5040,X5041,X5042] :
( ~ class_Rings_Olinordered__semidom(X5042)
| ~ c_Orderings_Oord__class_Oless(X5042,hAPP(hAPP(c_Power_Opower__class_Opower(X5042),X5041),X5040),hAPP(hAPP(c_Power_Opower__class_Opower(X5042),X5039),X5040))
| ~ c_Orderings_Oord__class_Oless__eq(X5042,c_Groups_Ozero__class_Ozero(X5042),X5039)
| c_Orderings_Oord__class_Oless(X5042,X5041,X5039) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).
fof(i_0_1532,plain,
! [X4389,X4390,X4391,X4392] :
( ~ class_Rings_Olinordered__semiring(X4392)
| ~ c_Orderings_Oord__class_Oless(X4392,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4392),X4391),X4390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4392),X4391),X4389))
| ~ c_Orderings_Oord__class_Oless__eq(X4392,c_Groups_Ozero__class_Ozero(X4392),X4391)
| c_Orderings_Oord__class_Oless(X4392,X4390,X4389) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).
fof(i_0_1533,plain,
! [X4393,X4394,X4395,X4396] :
( ~ class_Rings_Olinordered__semiring__strict(X4396)
| ~ c_Orderings_Oord__class_Oless(X4396,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4396),X4395),X4394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4396),X4395),X4393))
| ~ c_Orderings_Oord__class_Oless__eq(X4396,c_Groups_Ozero__class_Ozero(X4396),X4395)
| c_Orderings_Oord__class_Oless(X4396,X4394,X4393) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).
fof(i_0_1534,plain,
! [X4226,X4227,X4228,X4229] :
( ( ~ c_Orderings_Oord__class_Oless(X4229,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),X4228),X4227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),X4228),X4226))
| c_Orderings_Oord__class_Oless(X4229,X4227,X4226)
| ~ c_Orderings_Oord__class_Oless(X4229,c_Groups_Ozero__class_Ozero(X4229),X4228)
| ~ class_Rings_Olinordered__ring__strict(X4229) )
& ( ~ c_Orderings_Oord__class_Oless(X4229,X4227,X4226)
| c_Orderings_Oord__class_Oless(X4229,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),X4228),X4227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),X4228),X4226))
| ~ c_Orderings_Oord__class_Oless(X4229,c_Groups_Ozero__class_Ozero(X4229),X4228)
| ~ class_Rings_Olinordered__ring__strict(X4229) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).
fof(i_0_1535,plain,
! [X4397,X4398,X4399,X4400] :
( ~ class_Rings_Olinordered__semiring__strict(X4400)
| ~ c_Orderings_Oord__class_Oless__eq(X4400,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4400),X4399),X4398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4400),X4397),X4398))
| ~ c_Orderings_Oord__class_Oless(X4400,c_Groups_Ozero__class_Ozero(X4400),X4398)
| c_Orderings_Oord__class_Oless__eq(X4400,X4399,X4397) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).
fof(i_0_1536,plain,
! [X4401,X4402,X4403,X4404] :
( ~ class_Rings_Olinordered__semiring__strict(X4404)
| ~ c_Orderings_Oord__class_Oless__eq(X4404,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4404),X4403),X4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4404),X4403),X4401))
| ~ c_Orderings_Oord__class_Oless(X4404,c_Groups_Ozero__class_Ozero(X4404),X4403)
| c_Orderings_Oord__class_Oless__eq(X4404,X4402,X4401) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).
fof(i_0_1537,plain,
! [X4353,X4354,X4355,X4356] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4356,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4356),X4355),X4354),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4356),X4355),X4353))
| c_Orderings_Oord__class_Oless__eq(X4356,X4354,X4353)
| ~ c_Orderings_Oord__class_Oless(X4356,c_Groups_Ozero__class_Ozero(X4356),X4355)
| ~ class_Rings_Olinordered__ring__strict(X4356) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4356,X4354,X4353)
| c_Orderings_Oord__class_Oless__eq(X4356,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4356),X4355),X4354),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4356),X4355),X4353))
| ~ c_Orderings_Oord__class_Oless(X4356,c_Groups_Ozero__class_Ozero(X4356),X4355)
| ~ class_Rings_Olinordered__ring__strict(X4356) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).
fof(i_0_1538,plain,
! [X4245,X4246,X4247,X4248] :
( ( ~ c_Orderings_Oord__class_Oless(X4248,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4248),X4247),X4246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4248),X4247),X4245))
| c_Orderings_Oord__class_Oless(X4248,X4245,X4246)
| ~ c_Orderings_Oord__class_Oless(X4248,X4247,c_Groups_Ozero__class_Ozero(X4248))
| ~ class_Rings_Olinordered__ring__strict(X4248) )
& ( ~ c_Orderings_Oord__class_Oless(X4248,X4245,X4246)
| c_Orderings_Oord__class_Oless(X4248,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4248),X4247),X4246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4248),X4247),X4245))
| ~ c_Orderings_Oord__class_Oless(X4248,X4247,c_Groups_Ozero__class_Ozero(X4248))
| ~ class_Rings_Olinordered__ring__strict(X4248) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).
fof(i_0_1539,plain,
! [X4357,X4358,X4359,X4360] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4360),X4359),X4358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4360),X4359),X4357))
| c_Orderings_Oord__class_Oless__eq(X4360,X4357,X4358)
| ~ c_Orderings_Oord__class_Oless(X4360,X4359,c_Groups_Ozero__class_Ozero(X4360))
| ~ class_Rings_Olinordered__ring__strict(X4360) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4360,X4357,X4358)
| c_Orderings_Oord__class_Oless__eq(X4360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4360),X4359),X4358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4360),X4359),X4357))
| ~ c_Orderings_Oord__class_Oless(X4360,X4359,c_Groups_Ozero__class_Ozero(X4360))
| ~ class_Rings_Olinordered__ring__strict(X4360) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).
fof(i_0_1540,plain,
! [X5069,X5070,X5071,X5072] :
( ~ class_Rings_Olinordered__semidom(X5072)
| ~ c_Orderings_Oord__class_Oless(X5072,c_Groups_Oone__class_Oone(X5072),X5071)
| ~ c_Orderings_Oord__class_Oless(X5072,hAPP(hAPP(c_Power_Opower__class_Opower(X5072),X5071),X5070),hAPP(hAPP(c_Power_Opower__class_Opower(X5072),X5071),X5069))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5070,X5069) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_1541,plain,
! [X5065,X5066,X5067,X5068] :
( ( ~ c_Orderings_Oord__class_Oless(X5068,hAPP(hAPP(c_Power_Opower__class_Opower(X5068),X5067),X5066),hAPP(hAPP(c_Power_Opower__class_Opower(X5068),X5067),X5065))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5066,X5065)
| ~ c_Orderings_Oord__class_Oless(X5068,c_Groups_Oone__class_Oone(X5068),X5067)
| ~ class_Rings_Olinordered__semidom(X5068) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5066,X5065)
| c_Orderings_Oord__class_Oless(X5068,hAPP(hAPP(c_Power_Opower__class_Opower(X5068),X5067),X5066),hAPP(hAPP(c_Power_Opower__class_Opower(X5068),X5067),X5065))
| ~ c_Orderings_Oord__class_Oless(X5068,c_Groups_Oone__class_Oone(X5068),X5067)
| ~ class_Rings_Olinordered__semidom(X5068) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_1542,plain,
! [X5103,X5104,X5105,X5106] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5106,hAPP(hAPP(c_Power_Opower__class_Opower(X5106),X5105),X5104),hAPP(hAPP(c_Power_Opower__class_Opower(X5106),X5105),X5103))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5104,X5103)
| ~ c_Orderings_Oord__class_Oless(X5106,c_Groups_Oone__class_Oone(X5106),X5105)
| ~ class_Rings_Olinordered__semidom(X5106) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5104,X5103)
| c_Orderings_Oord__class_Oless__eq(X5106,hAPP(hAPP(c_Power_Opower__class_Opower(X5106),X5105),X5104),hAPP(hAPP(c_Power_Opower__class_Opower(X5106),X5105),X5103))
| ~ c_Orderings_Oord__class_Oless(X5106,c_Groups_Oone__class_Oone(X5106),X5105)
| ~ class_Rings_Olinordered__semidom(X5106) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).
fof(i_0_1543,plain,
! [X5099,X5100,X5101,X5102] :
( ~ class_Rings_Olinordered__semidom(X5102)
| ~ c_Orderings_Oord__class_Oless(X5102,c_Groups_Oone__class_Oone(X5102),X5101)
| ~ c_Orderings_Oord__class_Oless__eq(X5102,hAPP(hAPP(c_Power_Opower__class_Opower(X5102),X5101),X5100),hAPP(hAPP(c_Power_Opower__class_Opower(X5102),X5101),X5099))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5100,X5099) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).
fof(i_0_1544,plain,
! [X3453,X3454,X3455,X3456,X3457] :
( ~ class_Groups_Oab__group__add(X3457)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3457),c_Polynomial_OpCons(X3457,X3456,X3455),c_Polynomial_OpCons(X3457,X3454,X3453)) = c_Polynomial_OpCons(X3457,c_Groups_Ominus__class_Ominus(X3457,X3456,X3454),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3457),X3455,X3453)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__pCons])]) ).
fof(i_0_1545,plain,
! [X2943,X2944,X2945,X2946,X2947] :
( ~ class_Groups_Ocomm__monoid__add(X2947)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2947),c_Polynomial_OpCons(X2947,X2946,X2945),c_Polynomial_OpCons(X2947,X2944,X2943)) = c_Polynomial_OpCons(X2947,c_Groups_Oplus__class_Oplus(X2947,X2946,X2944),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2947),X2945,X2943)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pCons])]) ).
fof(i_0_1546,plain,
! [X4543,X4544,X4545,X4546] :
( ~ class_Rings_Ocomm__semiring__1(X4546)
| hAPP(c_Polynomial_Opoly(X4546,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X4546)),X4545),X4544)),X4543) = hAPP(hAPP(c_Power_Opower__class_Opower(X4546),hAPP(c_Polynomial_Opoly(X4546,X4545),X4543)),X4544) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__power])]) ).
fof(i_0_1547,plain,
! [X4495,X4496] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4496)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4495)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X4496)),c_RComplete_Onatfloor(X4495)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4496),X4495))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mult__natfloor])]) ).
fof(i_0_1548,plain,
! [X3890,X3891,X3892,X3893,X3894] :
( ~ class_Groups_Oab__group__add(X3894)
| c_Groups_Ominus__class_Ominus(X3894,c_Groups_Oplus__class_Oplus(X3894,X3893,X3892),c_Groups_Oplus__class_Oplus(X3894,X3891,X3890)) = c_Groups_Oplus__class_Oplus(X3894,c_Groups_Ominus__class_Ominus(X3894,X3893,X3891),c_Groups_Ominus__class_Ominus(X3894,X3892,X3890)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add])]) ).
fof(i_0_1549,plain,
! [X3204,X3205,X3206,X3207,X3208] :
( ~ class_Rings_Ocomm__semiring__1(X3208)
| c_Groups_Oplus__class_Oplus(X3208,c_Groups_Oplus__class_Oplus(X3208,X3207,X3206),c_Groups_Oplus__class_Oplus(X3208,X3205,X3204)) = c_Groups_Oplus__class_Oplus(X3208,c_Groups_Oplus__class_Oplus(X3208,X3207,X3205),c_Groups_Oplus__class_Oplus(X3208,X3206,X3204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_1550,plain,
! [X5087,X5088,X5089,X5090] :
( ~ class_Rings_Olinordered__semidom(X5090)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5089,X5088)
| ~ c_Orderings_Oord__class_Oless(X5090,c_Groups_Ozero__class_Ozero(X5090),X5087)
| ~ c_Orderings_Oord__class_Oless(X5090,X5087,c_Groups_Oone__class_Oone(X5090))
| c_Orderings_Oord__class_Oless(X5090,hAPP(hAPP(c_Power_Opower__class_Opower(X5090),X5087),X5088),hAPP(hAPP(c_Power_Opower__class_Opower(X5090),X5087),X5089)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_1551,plain,
! [X5095,X5096,X5097,X5098] :
( ~ class_Rings_Olinordered__semidom(X5098)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5097,X5096)
| ~ c_Orderings_Oord__class_Oless__eq(X5098,c_Groups_Ozero__class_Ozero(X5098),X5095)
| ~ c_Orderings_Oord__class_Oless__eq(X5098,X5095,c_Groups_Oone__class_Oone(X5098))
| c_Orderings_Oord__class_Oless__eq(X5098,hAPP(hAPP(c_Power_Opower__class_Opower(X5098),X5095),X5096),hAPP(hAPP(c_Power_Opower__class_Opower(X5098),X5095),X5097)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).
fof(i_0_1552,plain,
! [X5638,X5639,X5640,X5641] :
( ~ class_Divides_Osemiring__div(X5641)
| X5640 = c_Groups_Ozero__class_Ozero(X5641)
| c_Divides_Odiv__class_Odiv(X5641,c_Groups_Oplus__class_Oplus(X5641,X5639,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5641),X5640),X5638)),X5640) = c_Groups_Oplus__class_Oplus(X5641,X5638,c_Divides_Odiv__class_Odiv(X5641,X5639,X5640)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])]) ).
fof(i_0_1553,plain,
! [X5634,X5635,X5636,X5637] :
( ~ class_Divides_Osemiring__div(X5637)
| X5636 = c_Groups_Ozero__class_Ozero(X5637)
| c_Divides_Odiv__class_Odiv(X5637,c_Groups_Oplus__class_Oplus(X5637,X5635,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5637),X5634),X5636)),X5636) = c_Groups_Oplus__class_Oplus(X5637,X5634,c_Divides_Odiv__class_Odiv(X5637,X5635,X5636)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1])]) ).
fof(i_0_1554,plain,
! [X4940,X4941,X4942,X4943] :
( ~ class_Rings_Olinordered__semidom(X4943)
| ~ c_Orderings_Oord__class_Oless(X4943,X4942,X4941)
| ~ c_Orderings_Oord__class_Oless__eq(X4943,c_Groups_Ozero__class_Ozero(X4943),X4942)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4940)
| c_Orderings_Oord__class_Oless(X4943,hAPP(hAPP(c_Power_Opower__class_Opower(X4943),X4942),X4940),hAPP(hAPP(c_Power_Opower__class_Opower(X4943),X4941),X4940)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).
fof(i_0_1555,plain,
! [X4222,X4223,X4224,X4225] :
( ( c_Orderings_Oord__class_Oless(X4225,X4224,c_Groups_Ozero__class_Ozero(X4225))
| c_Orderings_Oord__class_Oless(X4225,c_Groups_Ozero__class_Ozero(X4225),X4224)
| ~ c_Orderings_Oord__class_Oless(X4225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4222))
| ~ class_Rings_Olinordered__ring__strict(X4225) )
& ( c_Orderings_Oord__class_Oless(X4225,X4222,X4223)
| c_Orderings_Oord__class_Oless(X4225,c_Groups_Ozero__class_Ozero(X4225),X4224)
| ~ c_Orderings_Oord__class_Oless(X4225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4222))
| ~ class_Rings_Olinordered__ring__strict(X4225) )
& ( c_Orderings_Oord__class_Oless(X4225,X4224,c_Groups_Ozero__class_Ozero(X4225))
| c_Orderings_Oord__class_Oless(X4225,X4223,X4222)
| ~ c_Orderings_Oord__class_Oless(X4225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4222))
| ~ class_Rings_Olinordered__ring__strict(X4225) )
& ( c_Orderings_Oord__class_Oless(X4225,X4222,X4223)
| c_Orderings_Oord__class_Oless(X4225,X4223,X4222)
| ~ c_Orderings_Oord__class_Oless(X4225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4222))
| ~ class_Rings_Olinordered__ring__strict(X4225) )
& ( ~ c_Orderings_Oord__class_Oless(X4225,c_Groups_Ozero__class_Ozero(X4225),X4224)
| ~ c_Orderings_Oord__class_Oless(X4225,X4223,X4222)
| c_Orderings_Oord__class_Oless(X4225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4222))
| ~ class_Rings_Olinordered__ring__strict(X4225) )
& ( ~ c_Orderings_Oord__class_Oless(X4225,X4224,c_Groups_Ozero__class_Ozero(X4225))
| ~ c_Orderings_Oord__class_Oless(X4225,X4222,X4223)
| c_Orderings_Oord__class_Oless(X4225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4222))
| ~ class_Rings_Olinordered__ring__strict(X4225) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).
fof(i_0_1556,plain,
! [X4218,X4219,X4220,X4221] :
( ( c_Orderings_Oord__class_Oless(X4221,X4219,c_Groups_Ozero__class_Ozero(X4221))
| c_Orderings_Oord__class_Oless(X4221,c_Groups_Ozero__class_Ozero(X4221),X4219)
| ~ c_Orderings_Oord__class_Oless(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4218),X4219))
| ~ class_Rings_Olinordered__ring__strict(X4221) )
& ( c_Orderings_Oord__class_Oless(X4221,X4218,X4220)
| c_Orderings_Oord__class_Oless(X4221,c_Groups_Ozero__class_Ozero(X4221),X4219)
| ~ c_Orderings_Oord__class_Oless(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4218),X4219))
| ~ class_Rings_Olinordered__ring__strict(X4221) )
& ( c_Orderings_Oord__class_Oless(X4221,X4219,c_Groups_Ozero__class_Ozero(X4221))
| c_Orderings_Oord__class_Oless(X4221,X4220,X4218)
| ~ c_Orderings_Oord__class_Oless(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4218),X4219))
| ~ class_Rings_Olinordered__ring__strict(X4221) )
& ( c_Orderings_Oord__class_Oless(X4221,X4218,X4220)
| c_Orderings_Oord__class_Oless(X4221,X4220,X4218)
| ~ c_Orderings_Oord__class_Oless(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4218),X4219))
| ~ class_Rings_Olinordered__ring__strict(X4221) )
& ( ~ c_Orderings_Oord__class_Oless(X4221,c_Groups_Ozero__class_Ozero(X4221),X4219)
| ~ c_Orderings_Oord__class_Oless(X4221,X4220,X4218)
| c_Orderings_Oord__class_Oless(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4218),X4219))
| ~ class_Rings_Olinordered__ring__strict(X4221) )
& ( ~ c_Orderings_Oord__class_Oless(X4221,X4219,c_Groups_Ozero__class_Ozero(X4221))
| ~ c_Orderings_Oord__class_Oless(X4221,X4218,X4220)
| c_Orderings_Oord__class_Oless(X4221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4218),X4219))
| ~ class_Rings_Olinordered__ring__strict(X4221) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).
fof(i_0_1557,plain,
! [X5518,X5519,X5521] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk24_2(X5518,X5519))
| ~ class_RealVector_Oreal__normed__algebra(X5519) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5519,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5519),X5521),X5518)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5519,X5521)),esk24_2(X5518,X5519)))
| ~ class_RealVector_Oreal__normed__algebra(X5519) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Opos__bounded])])])])]) ).
fof(i_0_1558,plain,
! [X3915,X3916,X3918] :
( ~ class_RealVector_Oreal__normed__algebra(X3916)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3916,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3916),X3918),X3915)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3916,X3918)),esk12_2(X3915,X3916))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Obounded])])])]) ).
fof(i_0_1559,plain,
! [X3903,X3904,X3906] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk9_2(X3903,X3904))
| ~ class_RealVector_Oreal__normed__algebra(X3904) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3904,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3904),X3906),X3903)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3904,X3906)),esk9_2(X3903,X3904)))
| ~ class_RealVector_Oreal__normed__algebra(X3904) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ononneg__bounded])])])])]) ).
fof(i_0_1560,plain,
! [X3501,X3502,X3503] :
( ~ class_RealVector_Oreal__normed__algebra(X3503)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3503,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3503),X3502),X3501)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3503,X3502)),c_RealVector_Onorm__class_Onorm(X3503,X3501))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])]) ).
fof(i_0_1561,plain,
! [X5514,X5515,X5517] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk23_2(X5514,X5515))
| ~ class_RealVector_Oreal__normed__algebra(X5515) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5515,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5515),X5514),X5517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5515,X5517)),esk23_2(X5514,X5515)))
| ~ class_RealVector_Oreal__normed__algebra(X5515) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Opos__bounded])])])])]) ).
fof(i_0_1562,plain,
! [X3911,X3912,X3914] :
( ~ class_RealVector_Oreal__normed__algebra(X3912)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3912,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3912),X3911),X3914)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3912,X3914)),esk11_2(X3911,X3912))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Obounded])])])]) ).
fof(i_0_1563,plain,
! [X3899,X3900,X3902] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk8_2(X3899,X3900))
| ~ class_RealVector_Oreal__normed__algebra(X3900) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3900),X3899),X3902)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3900,X3902)),esk8_2(X3899,X3900)))
| ~ class_RealVector_Oreal__normed__algebra(X3900) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ononneg__bounded])])])])]) ).
fof(i_0_1564,plain,
! [X3561,X3562,X3563,X3564] :
( ~ class_Rings_Ocomm__semiring__1(X3564)
| c_Groups_Oplus__class_Oplus(X3564,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3564),X3563),X3562),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3564),X3561),X3562)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3564),c_Groups_Oplus__class_Oplus(X3564,X3563,X3561)),X3562) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).
fof(i_0_1565,plain,
! [X3413,X3414,X3415,X3416] :
( ~ class_RealVector_Oreal__normed__algebra(X3416)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3416),c_Groups_Ominus__class_Ominus(X3416,X3415,X3414)),X3413) = c_Groups_Ominus__class_Ominus(X3416,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3416),X3415),X3413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3416),X3414),X3413)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left])]) ).
fof(i_0_1566,plain,
! [X3409,X3410,X3411,X3412] :
( ~ class_RealVector_Oreal__normed__algebra(X3412)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3412),c_Groups_Ominus__class_Ominus(X3412,X3411,X3410)),X3409) = c_Groups_Ominus__class_Ominus(X3412,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3412),X3411),X3409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3412),X3410),X3409)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff])]) ).
fof(i_0_1567,plain,
! [X3771,X3772,X3773,X3774] :
( ~ class_Rings_Ocomm__semiring(X3774)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3774),c_Groups_Oplus__class_Oplus(X3774,X3773,X3772)),X3771) = c_Groups_Oplus__class_Oplus(X3774,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3774),X3773),X3771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3774),X3772),X3771)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_1568,plain,
! [X3544,X3545,X3546,X3547] :
( ~ class_RealVector_Oreal__normed__algebra(X3547)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3547),c_Groups_Oplus__class_Oplus(X3547,X3546,X3545)),X3544) = c_Groups_Oplus__class_Oplus(X3547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3547),X3546),X3544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3547),X3545),X3544)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).
fof(i_0_1569,plain,
! [X3540,X3541,X3542,X3543] :
( ~ class_RealVector_Oreal__normed__algebra(X3543)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3543),c_Groups_Oplus__class_Oplus(X3543,X3542,X3541)),X3540) = c_Groups_Oplus__class_Oplus(X3543,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3543),X3542),X3540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3543),X3541),X3540)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).
fof(i_0_1570,plain,
! [X3565,X3566,X3567,X3568] :
( ~ class_Rings_Ocomm__semiring__1(X3568)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3568),c_Groups_Oplus__class_Oplus(X3568,X3567,X3566)),X3565) = c_Groups_Oplus__class_Oplus(X3568,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3568),X3567),X3565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3568),X3566),X3565)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
cnf(i_0_1571,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1269]) ).
fof(i_0_1572,plain,
! [X5704,X5705,X5706] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5706)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5705)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5705,X5704)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5706,X5704),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5706,X5705)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).
fof(i_0_1573,plain,
! [X5715,X5716,X5717] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5717,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5716)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5716,X5715)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5717,X5716),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5717,X5715)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).
fof(i_0_1574,plain,
! [X4788,X4789,X4790,X4791] :
( ~ class_Rings_Ocomm__semiring__1(X4791)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4791),hAPP(hAPP(c_Power_Opower__class_Opower(X4791),X4790),X4789)),hAPP(hAPP(c_Power_Opower__class_Opower(X4791),X4790),X4788)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4791),X4790),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4789,X4788)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).
fof(i_0_1575,plain,
! [X5033,X5034,X5035,X5036] :
( ~ class_Groups_Omonoid__mult(X5036)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5036),X5035),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5034,X5033)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5036),hAPP(hAPP(c_Power_Opower__class_Opower(X5036),X5035),X5034)),hAPP(hAPP(c_Power_Opower__class_Opower(X5036),X5035),X5033)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_1576,plain,
! [X3367,X3368,X3369,X3370] :
( ~ class_Rings_Ocomm__semiring__1(X3370)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3370),X3369),X3368)),X3367) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3370),X3369),X3367)),X3368) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
fof(i_0_1577,plain,
! [X5676,X5677,X5678,X5679] :
( ~ class_Divides_Osemiring__div(X5679)
| ~ c_Rings_Odvd__class_Odvd(X5679,X5678,X5677)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),c_Divides_Odiv__class_Odiv(X5679,X5677,X5678)),X5676) = c_Divides_Odiv__class_Odiv(X5679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5677),X5676),X5678) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult])]) ).
fof(i_0_1578,plain,
! [X3614,X3615,X3616,X3617,X3618,X3619] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3619)
| X3618 = c_Groups_Ozero__class_Ozero(X3619)
| X3617 != X3616
| X3615 = X3614
| c_Groups_Oplus__class_Oplus(X3619,X3617,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3619),X3618),X3615)) != c_Groups_Oplus__class_Oplus(X3619,X3616,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3619),X3618),X3614)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
fof(i_0_1579,plain,
! [X5413,X5414,X5415] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5415),X5414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5415),X5413))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5415)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5414,X5413) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel])]) ).
fof(i_0_1580,plain,
! [X5410,X5411,X5412] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5412),X5411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5412),X5410))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5411,X5410)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5412) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5411,X5410)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5412),X5411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5412),X5410))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5412) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1])])]) ).
fof(i_0_1581,plain,
! [X4994,X4995,X4996] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4996)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4996),X4995),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4996),X4994))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4995,X4994) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_1582,plain,
! [X4319,X4320,X4321] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4321),X4320),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4321),X4319))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4320,X4319)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4321) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4320,X4319)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4321),X4320),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4321),X4319))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4321) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_1583,plain,
! [X4869,X4870,X4871] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4870),X4871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4869),X4871))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4870,X4869)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4871) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4870,X4869)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4870),X4871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4869),X4871))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4871) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1])])]) ).
fof(i_0_1584,plain,
! [X4457,X4458,X4459] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4459),X4458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4457),X4458))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4458)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4459,X4457) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4458)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4459),X4458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4457),X4458)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4459,X4457)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4459),X4458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4457),X4458)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).
fof(i_0_1585,plain,
! [X5420,X5421,X5422] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5422),X5421),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5422),X5420))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5422)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5421,X5420) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le])]) ).
fof(i_0_1586,plain,
! [X4454,X4455,X4456] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4456),X4455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4456),X4454))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4456)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4455,X4454) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4456)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4456),X4455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4456),X4454)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4455,X4454)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4456),X4455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4456),X4454)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).
fof(i_0_1587,plain,
! [X4451,X4452,X4453] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4453),X4452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4453),X4451))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4452,X4451)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4453) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4452,X4451)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4453),X4452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4453),X4451))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4453) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).
fof(i_0_1588,plain,
! [X4915,X4916,X4917] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4916),X4917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4915),X4917))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4916,X4915)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4917) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4916,X4915)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4916),X4917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4915),X4917))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4917) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1])])]) ).
fof(i_0_1589,plain,
! [X4918,X4919,X4920] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4920),X4919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4920),X4918))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4919,X4918)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4920) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4919,X4918)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4920),X4919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4920),X4918))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4920) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2])])]) ).
fof(i_0_1590,plain,
! [X5529,X5530] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5530),X5529)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5529,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5530),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatceiling(X5529) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5530,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__eq])]) ).
fof(i_0_1591,plain,
! [X3498,X3499,X3500] :
( ~ class_RealVector_Oreal__normed__vector(X3500)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3500,X3499),c_RealVector_Onorm__class_Onorm(X3500,X3498)),c_RealVector_Onorm__class_Onorm(X3500,c_Groups_Ominus__class_Ominus(X3500,X3499,X3498))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2])]) ).
fof(i_0_1592,plain,
! [X3646,X3647,X3648] :
( ~ class_RealVector_Oreal__normed__vector(X3648)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3648,X3647),c_RealVector_Onorm__class_Onorm(X3648,X3646)),c_RealVector_Onorm__class_Onorm(X3648,c_Groups_Oplus__class_Oplus(X3648,X3647,X3646))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq])]) ).
fof(i_0_1593,plain,
! [X3649,X3650,X3651] :
( ~ class_RealVector_Oreal__normed__vector(X3651)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3651,c_Groups_Ominus__class_Ominus(X3651,X3650,X3649)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3651,X3650),c_RealVector_Onorm__class_Onorm(X3651,X3649))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq4])]) ).
fof(i_0_1594,plain,
! [X2934,X2935,X2936] :
( ~ class_RealVector_Oreal__normed__vector(X2936)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2936,c_Groups_Oplus__class_Oplus(X2936,X2935,X2934)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2936,X2935),c_RealVector_Onorm__class_Onorm(X2936,X2934))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq])]) ).
fof(i_0_1595,plain,
! [X3425,X3426,X3427,X3428] :
( ~ class_Rings_Ocomm__semiring__0(X3428)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3428)),c_Polynomial_Osmult(X3428,X3427,X3426)),X3425) = c_Polynomial_Osmult(X3428,X3427,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3428)),X3426),X3425)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__left])]) ).
fof(i_0_1596,plain,
! [X3465,X3466,X3467,X3468] :
( ~ class_Rings_Ocomm__ring(X3468)
| hAPP(c_Polynomial_Opoly(X3468,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3468),X3467,X3466)),X3465) = c_Groups_Ominus__class_Ominus(X3468,hAPP(c_Polynomial_Opoly(X3468,X3467),X3465),hAPP(c_Polynomial_Opoly(X3468,X3466),X3465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__diff])]) ).
fof(i_0_1597,plain,
! [X2939,X2940,X2941,X2942] :
( ~ class_Rings_Ocomm__semiring__0(X2942)
| hAPP(c_Polynomial_Opoly(X2942,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2942),X2941,X2940)),X2939) = c_Groups_Oplus__class_Oplus(X2942,hAPP(c_Polynomial_Opoly(X2942,X2941),X2939),hAPP(c_Polynomial_Opoly(X2942,X2940),X2939)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__add])]) ).
fof(i_0_1598,plain,
! [X5229,X5230,X5231,X5232,X5233] :
( ~ class_Rings_Ocomm__semiring__1(X5233)
| ~ c_Rings_Odvd__class_Odvd(X5233,hAPP(hAPP(c_Power_Opower__class_Opower(X5233),X5232),X5231),X5230)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5229,X5231)
| c_Rings_Odvd__class_Odvd(X5233,hAPP(hAPP(c_Power_Opower__class_Opower(X5233),X5232),X5229),X5230) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__dvd])]) ).
fof(i_0_1599,plain,
! [X3304,X3305,X3306] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3304,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3305,X3306))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3304,X3306),X3305)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3306,X3305) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3304,X3306),X3305)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3304,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3305,X3306))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3306,X3305) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).
fof(i_0_1600,plain,
! [X4966,X4967,X4968] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4968,X4967)),X4966) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4968),X4966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4967),X4966)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).
fof(i_0_1601,plain,
! [X4963,X4964,X4965] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4965,X4964)),X4963) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4965),X4963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4964),X4963)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_1602,plain,
! [X3744,X3745,X3746] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3746,X3745)),X3744) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3746),X3744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3745),X3744)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).
fof(i_0_1603,plain,
! [X3718,X3719,X3720] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3720,X3719)),X3718) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3720),X3718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3719),X3718)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(i_0_1604,plain,
! [X3588,X3589,X3590] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3590,X3589)),X3588) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3590),X3588),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3589),X3588)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
cnf(i_0_1605,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1270]) ).
fof(i_0_1606,plain,
! [X4559,X4560,X4561] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4561)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4561,hAPP(hAPP(c_Power_Opower__class_Opower(X4561),X4560),X4559)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4561,X4560)),X4559)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power__ineq])]) ).
fof(i_0_1607,plain,
! [X4124,X4125,X4126,X4127] :
( ( ~ c_Orderings_Oord__class_Oless(X4127,c_Groups_Oplus__class_Oplus(X4127,X4126,X4125),c_Groups_Oplus__class_Oplus(X4127,X4124,X4125))
| c_Orderings_Oord__class_Oless(X4127,X4126,X4124)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4127) )
& ( ~ c_Orderings_Oord__class_Oless(X4127,X4126,X4124)
| c_Orderings_Oord__class_Oless(X4127,c_Groups_Oplus__class_Oplus(X4127,X4126,X4125),c_Groups_Oplus__class_Oplus(X4127,X4124,X4125))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4127) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_1608,plain,
! [X4103,X4104,X4105,X4106] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4106)
| ~ c_Orderings_Oord__class_Oless(X4106,c_Groups_Oplus__class_Oplus(X4106,X4105,X4104),c_Groups_Oplus__class_Oplus(X4106,X4103,X4104))
| c_Orderings_Oord__class_Oless(X4106,X4105,X4103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_1609,plain,
! [X4120,X4121,X4122,X4123] :
( ( ~ c_Orderings_Oord__class_Oless(X4123,c_Groups_Oplus__class_Oplus(X4123,X4122,X4121),c_Groups_Oplus__class_Oplus(X4123,X4122,X4120))
| c_Orderings_Oord__class_Oless(X4123,X4121,X4120)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4123) )
& ( ~ c_Orderings_Oord__class_Oless(X4123,X4121,X4120)
| c_Orderings_Oord__class_Oless(X4123,c_Groups_Oplus__class_Oplus(X4123,X4122,X4121),c_Groups_Oplus__class_Oplus(X4123,X4122,X4120))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4123) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_1610,plain,
! [X4099,X4100,X4101,X4102] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4102)
| ~ c_Orderings_Oord__class_Oless(X4102,c_Groups_Oplus__class_Oplus(X4102,X4101,X4100),c_Groups_Oplus__class_Oplus(X4102,X4101,X4099))
| c_Orderings_Oord__class_Oless(X4102,X4100,X4099) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_1611,plain,
! [X3129,X3130,X3131,X3132] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3132)
| ~ c_Orderings_Oord__class_Oless__eq(X3132,c_Groups_Oplus__class_Oplus(X3132,X3131,X3130),c_Groups_Oplus__class_Oplus(X3132,X3129,X3130))
| c_Orderings_Oord__class_Oless__eq(X3132,X3131,X3129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_1612,plain,
! [X2951,X2952,X2953,X2954] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2954,c_Groups_Oplus__class_Oplus(X2954,X2953,X2952),c_Groups_Oplus__class_Oplus(X2954,X2951,X2952))
| c_Orderings_Oord__class_Oless__eq(X2954,X2953,X2951)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2954) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2954,X2953,X2951)
| c_Orderings_Oord__class_Oless__eq(X2954,c_Groups_Oplus__class_Oplus(X2954,X2953,X2952),c_Groups_Oplus__class_Oplus(X2954,X2951,X2952))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2954) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_1613,plain,
! [X3125,X3126,X3127,X3128] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3128)
| ~ c_Orderings_Oord__class_Oless__eq(X3128,c_Groups_Oplus__class_Oplus(X3128,X3127,X3126),c_Groups_Oplus__class_Oplus(X3128,X3127,X3125))
| c_Orderings_Oord__class_Oless__eq(X3128,X3126,X3125) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_1614,plain,
! [X2955,X2956,X2957,X2958] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2958,c_Groups_Oplus__class_Oplus(X2958,X2957,X2956),c_Groups_Oplus__class_Oplus(X2958,X2957,X2955))
| c_Orderings_Oord__class_Oless__eq(X2958,X2956,X2955)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2958) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2958,X2956,X2955)
| c_Orderings_Oord__class_Oless__eq(X2958,c_Groups_Oplus__class_Oplus(X2958,X2957,X2956),c_Groups_Oplus__class_Oplus(X2958,X2957,X2955))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2958) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
cnf(i_0_1615,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1271]) ).
cnf(i_0_1616,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1272]) ).
cnf(i_0_1617,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1273]) ).
cnf(i_0_1618,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(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),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1274]) ).
fof(i_0_1619,plain,
! [X3337,X3338,X3339] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3339,X3338)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3339,X3337)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3338,X3339),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3337,X3339)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3338,X3337) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).
fof(i_0_1620,plain,
! [X5312,X5313,X5314,X5315] :
( ( ~ c_Rings_Odvd__class_Odvd(X5315,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5315),X5314),X5313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5315),X5314),X5312))
| X5314 = c_Groups_Ozero__class_Ozero(X5315)
| c_Rings_Odvd__class_Odvd(X5315,X5313,X5312)
| ~ class_Rings_Oidom(X5315) )
& ( X5314 != c_Groups_Ozero__class_Ozero(X5315)
| c_Rings_Odvd__class_Odvd(X5315,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5315),X5314),X5313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5315),X5314),X5312))
| ~ class_Rings_Oidom(X5315) )
& ( ~ c_Rings_Odvd__class_Odvd(X5315,X5313,X5312)
| c_Rings_Odvd__class_Odvd(X5315,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5315),X5314),X5313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5315),X5314),X5312))
| ~ class_Rings_Oidom(X5315) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left])])]) ).
fof(i_0_1621,plain,
! [X5316,X5317,X5318,X5319] :
( ( ~ c_Rings_Odvd__class_Odvd(X5319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5319),X5318),X5317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5319),X5316),X5317))
| X5317 = c_Groups_Ozero__class_Ozero(X5319)
| c_Rings_Odvd__class_Odvd(X5319,X5318,X5316)
| ~ class_Rings_Oidom(X5319) )
& ( X5317 != c_Groups_Ozero__class_Ozero(X5319)
| c_Rings_Odvd__class_Odvd(X5319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5319),X5318),X5317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5319),X5316),X5317))
| ~ class_Rings_Oidom(X5319) )
& ( ~ c_Rings_Odvd__class_Odvd(X5319,X5318,X5316)
| c_Rings_Odvd__class_Odvd(X5319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5319),X5318),X5317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5319),X5316),X5317))
| ~ class_Rings_Oidom(X5319) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right])])]) ).
fof(i_0_1622,plain,
! [X5051,X5052,X5053] :
( ~ class_Rings_Olinordered__semidom(X5053)
| ~ c_Orderings_Oord__class_Oless(X5053,c_Groups_Oone__class_Oone(X5053),X5052)
| c_Orderings_Oord__class_Oless(X5053,c_Groups_Oone__class_Oone(X5053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5053),X5052),hAPP(hAPP(c_Power_Opower__class_Opower(X5053),X5052),X5051))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).
fof(i_0_1623,plain,
! [X5368,X5369,X5370] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5370,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5369,X5368))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5370,X5368)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5368,X5369)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5370,X5369) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diffD])]) ).
fof(i_0_1624,plain,
! [X5365,X5366,X5367] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5367,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5366,X5365))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5367,X5366)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5365,X5366)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5367,X5365) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diffD1])]) ).
fof(i_0_1625,plain,
! [X5652,X5653,X5654,X5655,X5656] :
( ( c_Divides_Odiv__class_Odiv(X5656,X5653,X5655) != c_Divides_Odiv__class_Odiv(X5656,X5652,X5654)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5656),X5653),X5654) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5656),X5655),X5652)
| ~ c_Rings_Odvd__class_Odvd(X5656,X5654,X5652)
| ~ c_Rings_Odvd__class_Odvd(X5656,X5655,X5653)
| X5654 = c_Groups_Ozero__class_Ozero(X5656)
| X5655 = c_Groups_Ozero__class_Ozero(X5656)
| ~ class_Divides_Osemiring__div(X5656) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5656),X5653),X5654) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5656),X5655),X5652)
| c_Divides_Odiv__class_Odiv(X5656,X5653,X5655) = c_Divides_Odiv__class_Odiv(X5656,X5652,X5654)
| ~ c_Rings_Odvd__class_Odvd(X5656,X5654,X5652)
| ~ c_Rings_Odvd__class_Odvd(X5656,X5655,X5653)
| X5654 = c_Groups_Ozero__class_Ozero(X5656)
| X5655 = c_Groups_Ozero__class_Ozero(X5656)
| ~ class_Divides_Osemiring__div(X5656) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__div__eq__mult])])]) ).
fof(i_0_1626,plain,
! [X4646,X4647,X4648] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4648),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4647,X4646)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4648),X4647)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4648),X4646)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(i_0_1627,plain,
! [X3231,X3232,X3233,X3234] :
( ~ class_Rings_Ocomm__semiring__0(X3234)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3234),c_Polynomial_Osmult(X3234,X3233,X3232),c_Polynomial_OpCons(X3234,X3231,X3232)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3234))
| X3232 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3234)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__lemma])]) ).
cnf(i_0_1628,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(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_1275]) ).
fof(i_0_1629,plain,
! [X4171,X4172,X4173] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4173,X4172),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4173,X4171))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4172,X4171) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4172,X4171)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4173,X4172),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4173,X4171)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_1630,plain,
! [X3263,X3264,X3265] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3265,X3264),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3265,X3263))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3264,X3263) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3264,X3263)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3265,X3264),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3265,X3263)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_1631,plain,
! [X5162,X5163,X5164] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5164)
| X5164 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5163,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5164),X5162))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5163)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5162,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2])]) ).
fof(i_0_1632,plain,
! [X5159,X5160,X5161] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5161)
| X5161 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5161),X5159))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5160,X5161)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5159) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).
fof(i_0_1633,plain,
! [X3437,X3438,X3439,X3440] :
( ~ class_Rings_Ocomm__ring(X3440)
| c_Polynomial_Osmult(X3440,X3439,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3440),X3438,X3437)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3440),c_Polynomial_Osmult(X3440,X3439,X3438),c_Polynomial_Osmult(X3440,X3439,X3437)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__diff__right])]) ).
fof(i_0_1634,plain,
! [X3595,X3596,X3597,X3598] :
( ~ class_Rings_Ocomm__semiring__0(X3598)
| c_Polynomial_Osmult(X3598,X3597,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3598),X3596,X3595)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3598),c_Polynomial_Osmult(X3598,X3597,X3596),c_Polynomial_Osmult(X3598,X3597,X3595)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__right])]) ).
fof(i_0_1635,plain,
! [X5091,X5092,X5093,X5094] :
( ~ class_Rings_Olinordered__semidom(X5094)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5094),X5093),X5092) != hAPP(hAPP(c_Power_Opower__class_Opower(X5094),X5091),X5092)
| ~ c_Orderings_Oord__class_Oless__eq(X5094,c_Groups_Ozero__class_Ozero(X5094),X5093)
| ~ c_Orderings_Oord__class_Oless__eq(X5094,c_Groups_Ozero__class_Ozero(X5094),X5091)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5092)
| X5093 = X5091 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).
fof(i_0_1636,plain,
! [X4311,X4312,X4313] :
( ~ class_Rings_Ocomm__semiring__1(X4313)
| c_Groups_Oplus__class_Oplus(X4313,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4313),X4312),X4311),X4311) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4313),c_Groups_Oplus__class_Oplus(X4313,X4312,c_Groups_Oone__class_Oone(X4313))),X4311) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
fof(i_0_1637,plain,
! [X4308,X4309,X4310] :
( ~ class_Rings_Ocomm__semiring__1(X4310)
| c_Groups_Oplus__class_Oplus(X4310,X4309,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4310),X4308),X4309)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4310),c_Groups_Oplus__class_Oplus(X4310,X4308,c_Groups_Oone__class_Oone(X4310))),X4309) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
fof(i_0_1638,plain,
! [X5588,X5589] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5589),X5588)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5588,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5589),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatfloor(X5588) = X5589 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__eq])]) ).
fof(i_0_1639,plain,
! [X4431,X4432,X4433] :
( ~ class_Rings_Olinordered__idom(X4433)
| ~ c_Orderings_Oord__class_Oless__eq(X4433,c_Groups_Ozero__class_Ozero(X4433),X4432)
| ~ c_Orderings_Oord__class_Oless__eq(X4433,c_Groups_Ozero__class_Ozero(X4433),X4431)
| ~ c_Orderings_Oord__class_Oless__eq(X4433,X4431,c_Groups_Oone__class_Oone(X4433))
| c_Orderings_Oord__class_Oless__eq(X4433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4433),X4432),X4431),X4432) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).
fof(i_0_1640,plain,
! [X4434,X4435,X4436] :
( ~ class_Rings_Olinordered__idom(X4436)
| ~ c_Orderings_Oord__class_Oless__eq(X4436,c_Groups_Ozero__class_Ozero(X4436),X4435)
| ~ c_Orderings_Oord__class_Oless__eq(X4436,c_Groups_Ozero__class_Ozero(X4436),X4434)
| ~ c_Orderings_Oord__class_Oless__eq(X4436,X4434,c_Groups_Oone__class_Oone(X4436))
| c_Orderings_Oord__class_Oless__eq(X4436,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4436),X4434),X4435),X4435) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).
fof(i_0_1641,plain,
! [X3659,X3660,X3661,X3662] :
( ~ class_RealVector_Oreal__normed__vector(X3662)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3661,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3662,X3660),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3661),c_RealVector_Onorm__class_Onorm(X3662,X3659)))
| X3660 = c_Groups_Ozero__class_Ozero(X3662) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ratiotest__lemma])]) ).
fof(i_0_1642,plain,
! [X4255,X4256,X4257,X4258] :
( ~ class_Rings_Olinordered__semiring__strict(X4258)
| ~ c_Orderings_Oord__class_Oless(X4258,X4257,X4256)
| ~ c_Orderings_Oord__class_Oless(X4258,c_Groups_Ozero__class_Ozero(X4258),X4255)
| c_Orderings_Oord__class_Oless(X4258,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4258),X4257),X4255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4258),X4256),X4255)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_1643,plain,
! [X4263,X4264,X4265,X4266] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X4266)
| ~ c_Orderings_Oord__class_Oless(X4266,X4265,X4264)
| ~ c_Orderings_Oord__class_Oless(X4266,c_Groups_Ozero__class_Ozero(X4266),X4263)
| c_Orderings_Oord__class_Oless(X4266,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4266),X4263),X4265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4266),X4263),X4264)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_1644,plain,
! [X4259,X4260,X4261,X4262] :
( ~ class_Rings_Olinordered__semiring__strict(X4262)
| ~ c_Orderings_Oord__class_Oless(X4262,X4261,X4260)
| ~ c_Orderings_Oord__class_Oless(X4262,c_Groups_Ozero__class_Ozero(X4262),X4259)
| c_Orderings_Oord__class_Oless(X4262,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4262),X4259),X4261),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4262),X4259),X4260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_1645,plain,
! [X5006,X5007,X5008,X5009] :
( ~ class_Rings_Olinordered__semidom(X5009)
| ~ c_Orderings_Oord__class_Oless__eq(X5009,X5008,X5007)
| ~ c_Orderings_Oord__class_Oless__eq(X5009,c_Groups_Ozero__class_Ozero(X5009),X5008)
| c_Orderings_Oord__class_Oless__eq(X5009,hAPP(hAPP(c_Power_Opower__class_Opower(X5009),X5008),X5006),hAPP(hAPP(c_Power_Opower__class_Opower(X5009),X5007),X5006)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).
fof(i_0_1646,plain,
! [X3812,X3813,X3814,X3815] :
( ~ class_Rings_Oordered__semiring(X3815)
| ~ c_Orderings_Oord__class_Oless__eq(X3815,X3814,X3813)
| ~ c_Orderings_Oord__class_Oless__eq(X3815,c_Groups_Ozero__class_Ozero(X3815),X3812)
| c_Orderings_Oord__class_Oless__eq(X3815,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3815),X3814),X3812),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3815),X3813),X3812)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).
fof(i_0_1647,plain,
! [X3804,X3805,X3806,X3807] :
( ~ class_Rings_Oordered__comm__semiring(X3807)
| ~ c_Orderings_Oord__class_Oless__eq(X3807,X3806,X3805)
| ~ c_Orderings_Oord__class_Oless__eq(X3807,c_Groups_Ozero__class_Ozero(X3807),X3804)
| c_Orderings_Oord__class_Oless__eq(X3807,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3807),X3804),X3806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3807),X3804),X3805)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).
fof(i_0_1648,plain,
! [X3808,X3809,X3810,X3811] :
( ~ class_Rings_Oordered__semiring(X3811)
| ~ c_Orderings_Oord__class_Oless__eq(X3811,X3810,X3809)
| ~ c_Orderings_Oord__class_Oless__eq(X3811,c_Groups_Ozero__class_Ozero(X3811),X3808)
| c_Orderings_Oord__class_Oless__eq(X3811,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3811),X3808),X3810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3811),X3808),X3809)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).
fof(i_0_1649,plain,
! [X4267,X4268,X4269,X4270] :
( ~ class_Rings_Olinordered__ring__strict(X4270)
| ~ c_Orderings_Oord__class_Oless(X4270,X4269,X4268)
| ~ c_Orderings_Oord__class_Oless(X4270,X4267,c_Groups_Ozero__class_Ozero(X4270))
| c_Orderings_Oord__class_Oless(X4270,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4270),X4268),X4267),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4270),X4269),X4267)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_1650,plain,
! [X4271,X4272,X4273,X4274] :
( ~ class_Rings_Olinordered__ring__strict(X4274)
| ~ c_Orderings_Oord__class_Oless(X4274,X4273,X4272)
| ~ c_Orderings_Oord__class_Oless(X4274,X4271,c_Groups_Ozero__class_Ozero(X4274))
| c_Orderings_Oord__class_Oless(X4274,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4274),X4271),X4272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4274),X4271),X4273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
fof(i_0_1651,plain,
! [X3800,X3801,X3802,X3803] :
( ~ class_Rings_Oordered__ring(X3803)
| ~ c_Orderings_Oord__class_Oless__eq(X3803,X3802,X3801)
| ~ c_Orderings_Oord__class_Oless__eq(X3803,X3800,c_Groups_Ozero__class_Ozero(X3803))
| c_Orderings_Oord__class_Oless__eq(X3803,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3803),X3801),X3800),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3803),X3802),X3800)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).
fof(i_0_1652,plain,
! [X3796,X3797,X3798,X3799] :
( ~ class_Rings_Oordered__ring(X3799)
| ~ c_Orderings_Oord__class_Oless__eq(X3799,X3798,X3797)
| ~ c_Orderings_Oord__class_Oless__eq(X3799,X3796,c_Groups_Ozero__class_Ozero(X3799))
| c_Orderings_Oord__class_Oless__eq(X3799,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3799),X3796),X3797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3799),X3796),X3798)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).
fof(i_0_1653,plain,
! [X3279,X3280,X3281] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3281,X3280)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3279,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3280,X3279),X3281)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).
fof(i_0_1654,plain,
! [X4107,X4108,X4109,X4110,X4111] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4111)
| ~ c_Orderings_Oord__class_Oless(X4111,X4110,X4109)
| ~ c_Orderings_Oord__class_Oless(X4111,X4108,X4107)
| c_Orderings_Oord__class_Oless(X4111,c_Groups_Oplus__class_Oplus(X4111,X4110,X4108),c_Groups_Oplus__class_Oplus(X4111,X4109,X4107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_1655,plain,
! [X4291,X4292,X4293,X4294,X4295] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4295)
| ~ c_Orderings_Oord__class_Oless__eq(X4295,X4294,X4293)
| ~ c_Orderings_Oord__class_Oless(X4295,X4292,X4291)
| c_Orderings_Oord__class_Oless(X4295,c_Groups_Oplus__class_Oplus(X4295,X4294,X4292),c_Groups_Oplus__class_Oplus(X4295,X4293,X4291)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_1656,plain,
! [X4296,X4297,X4298,X4299,X4300] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4300)
| ~ c_Orderings_Oord__class_Oless(X4300,X4299,X4298)
| ~ c_Orderings_Oord__class_Oless__eq(X4300,X4297,X4296)
| c_Orderings_Oord__class_Oless(X4300,c_Groups_Oplus__class_Oplus(X4300,X4299,X4297),c_Groups_Oplus__class_Oplus(X4300,X4298,X4296)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_1657,plain,
! [X2967,X2968,X2969,X2970,X2971] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2971)
| ~ c_Orderings_Oord__class_Oless__eq(X2971,X2970,X2969)
| ~ c_Orderings_Oord__class_Oless__eq(X2971,X2968,X2967)
| c_Orderings_Oord__class_Oless__eq(X2971,c_Groups_Oplus__class_Oplus(X2971,X2970,X2968),c_Groups_Oplus__class_Oplus(X2971,X2969,X2967)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_1658,plain,
! [X5073,X5074,X5075,X5076] :
( ~ class_Rings_Olinordered__semidom(X5076)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5075,X5074)
| ~ c_Orderings_Oord__class_Oless(X5076,c_Groups_Oone__class_Oone(X5076),X5073)
| c_Orderings_Oord__class_Oless(X5076,hAPP(hAPP(c_Power_Opower__class_Opower(X5076),X5073),X5075),hAPP(hAPP(c_Power_Opower__class_Opower(X5076),X5073),X5074)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_1659,plain,
! [X5077,X5078,X5079,X5080] :
( ~ class_Rings_Olinordered__semidom(X5080)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5079,X5078)
| ~ c_Orderings_Oord__class_Oless__eq(X5080,c_Groups_Oone__class_Oone(X5080),X5077)
| c_Orderings_Oord__class_Oless__eq(X5080,hAPP(hAPP(c_Power_Opower__class_Opower(X5080),X5077),X5079),hAPP(hAPP(c_Power_Opower__class_Opower(X5080),X5077),X5078)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).
fof(i_0_1660,plain,
! [X3401,X3402,X3403,X3404] :
( ~ class_Groups_Oab__group__add(X3404)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3404),c_Polynomial_Omonom(X3404,X3403,X3402),c_Polynomial_Omonom(X3404,X3401,X3402)) = c_Polynomial_Omonom(X3404,c_Groups_Ominus__class_Ominus(X3404,X3403,X3401),X3402) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__monom])]) ).
fof(i_0_1661,plain,
! [X3642,X3643,X3644,X3645] :
( ~ class_Groups_Ocomm__monoid__add(X3645)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3645),c_Polynomial_Omonom(X3645,X3644,X3643),c_Polynomial_Omonom(X3645,X3642,X3643)) = c_Polynomial_Omonom(X3645,c_Groups_Oplus__class_Oplus(X3645,X3644,X3642),X3643) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__monom])]) ).
fof(i_0_1662,plain,
! [X3417,X3418,X3419,X3420] :
( ~ class_Rings_Ocomm__ring(X3420)
| c_Polynomial_Osmult(X3420,c_Groups_Ominus__class_Ominus(X3420,X3419,X3418),X3417) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3420),c_Polynomial_Osmult(X3420,X3419,X3417),c_Polynomial_Osmult(X3420,X3418,X3417)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__diff__left])]) ).
fof(i_0_1663,plain,
! [X3633,X3634,X3635,X3636] :
( ~ class_Rings_Ocomm__semiring__0(X3636)
| c_Polynomial_Osmult(X3636,c_Groups_Oplus__class_Oplus(X3636,X3635,X3634),X3633) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3636),c_Polynomial_Osmult(X3636,X3635,X3633),c_Polynomial_Osmult(X3636,X3634,X3633)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__left])]) ).
fof(i_0_1664,plain,
! [X5261,X5262,X5263,X5264,X5265] :
( ~ class_Rings_Ocomm__semiring__1(X5265)
| ~ c_Rings_Odvd__class_Odvd(X5265,X5264,X5263)
| ~ c_Rings_Odvd__class_Odvd(X5265,X5262,X5261)
| c_Rings_Odvd__class_Odvd(X5265,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5265),X5264),X5262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5265),X5263),X5261)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono])]) ).
fof(i_0_1665,plain,
! [X4488,X4489,X4491] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk15_2(X4488,X4489),X4488)
| ~ hBOOL(hAPP(X4489,X4488))
| hBOOL(hAPP(X4489,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4491,esk15_2(X4488,X4489))
| ~ hBOOL(hAPP(X4489,X4491))
| ~ hBOOL(hAPP(X4489,X4488))
| hBOOL(hAPP(X4489,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X4489,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk15_2(X4488,X4489),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X4489,X4488))
| hBOOL(hAPP(X4489,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_1276])])])])]) ).
fof(i_0_1666,plain,
! [X4937,X4938,X4939] :
( ( X4938 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4939),X4937),X4938) = c_Groups_Oone__class_Oone(X4939)
| ~ class_Power_Opower(X4939) )
& ( X4938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4939),X4937),X4938) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4939),X4937),hAPP(hAPP(c_Power_Opower__class_Opower(X4939),X4937),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4938,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X4939) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if])])]) ).
fof(i_0_1667,plain,
! [X5234,X5235,X5236,X5237,X5238] :
( ~ class_Rings_Ocomm__semiring__1(X5238)
| ~ c_Rings_Odvd__class_Odvd(X5238,X5237,X5236)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5235,X5234)
| c_Rings_Odvd__class_Odvd(X5238,hAPP(hAPP(c_Power_Opower__class_Opower(X5238),X5237),X5235),hAPP(hAPP(c_Power_Opower__class_Opower(X5238),X5236),X5234)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__le])]) ).
cnf(i_0_1668,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1277]) ).
fof(i_0_1669,plain,
! [X5720,X5721,X5722] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5722,X5721)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5720)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5722,X5720),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5721,X5720)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).
fof(i_0_1670,plain,
! [X5723,X5724,X5725] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5725,X5724)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5723,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5724,X5723),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5725,X5723)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).
fof(i_0_1671,plain,
! [X3461,X3462,X3463,X3464] :
( ~ class_Rings_Ocomm__semiring__0(X3464)
| c_Polynomial_Osmult(X3464,X3463,c_Polynomial_OpCons(X3464,X3462,X3461)) = c_Polynomial_OpCons(X3464,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3464),X3463),X3462),c_Polynomial_Osmult(X3464,X3463,X3461)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__pCons])]) ).
fof(i_0_1672,plain,
! [X5122,X5123,X5124,X5125] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5125,X5124)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5123,X5122)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5125,X5123),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5124,X5122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).
fof(i_0_1673,plain,
! [X4345,X4346,X4347] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4347,X4346)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4345,X4347)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4347,X4345),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4346,X4345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).
fof(i_0_1674,plain,
! [X4196,X4197,X4198] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4198,X4197)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4198,X4196)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4196,X4197),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4196,X4198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).
fof(i_0_1675,plain,
! [X4158,X4159,X4160,X4161] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4161,X4160)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4159,X4158)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4161,X4159),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4160,X4158)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_1676,plain,
! [X3326,X3327,X3328,X3329] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3329,X3328)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3327,X3326)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3329,X3327),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3328,X3326)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_1677,plain,
! [X3695,X3696,X3697] :
( ( X3696 = c_Groups_Ozero__class_Ozero(X3697)
| c_Groups_Oplus__class_Oplus(X3697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3697),X3696),X3696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3697),X3695),X3695)) != c_Groups_Ozero__class_Ozero(X3697)
| ~ class_Rings_Olinordered__ring__strict(X3697) )
& ( X3695 = c_Groups_Ozero__class_Ozero(X3697)
| c_Groups_Oplus__class_Oplus(X3697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3697),X3696),X3696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3697),X3695),X3695)) != c_Groups_Ozero__class_Ozero(X3697)
| ~ class_Rings_Olinordered__ring__strict(X3697) )
& ( X3696 != c_Groups_Ozero__class_Ozero(X3697)
| X3695 != c_Groups_Ozero__class_Ozero(X3697)
| c_Groups_Oplus__class_Oplus(X3697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3697),X3696),X3696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3697),X3695),X3695)) = c_Groups_Ozero__class_Ozero(X3697)
| ~ class_Rings_Olinordered__ring__strict(X3697) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).
cnf(i_0_1678,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]) ).
cnf(i_0_1679,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1279]) ).
fof(i_0_1680,plain,
! [X3433,X3434,X3435,X3436] :
( ~ class_RealVector_Oreal__normed__algebra(X3436)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3436),X3435),c_Groups_Ominus__class_Ominus(X3436,X3434,X3433)) = c_Groups_Ominus__class_Ominus(X3436,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3436),X3435),X3434),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3436),X3435),X3433)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right])]) ).
fof(i_0_1681,plain,
! [X3429,X3430,X3431,X3432] :
( ~ class_RealVector_Oreal__normed__algebra(X3432)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3432),X3431),c_Groups_Ominus__class_Ominus(X3432,X3430,X3429)) = c_Groups_Ominus__class_Ominus(X3432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3432),X3431),X3430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3432),X3431),X3429)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff])]) ).
fof(i_0_1682,plain,
! [X3552,X3553,X3554,X3555] :
( ~ class_RealVector_Oreal__normed__algebra(X3555)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3555),X3554),c_Groups_Oplus__class_Oplus(X3555,X3553,X3552)) = c_Groups_Oplus__class_Oplus(X3555,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3555),X3554),X3553),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3555),X3554),X3552)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).
fof(i_0_1683,plain,
! [X3548,X3549,X3550,X3551] :
( ~ class_RealVector_Oreal__normed__algebra(X3551)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3551),X3550),c_Groups_Oplus__class_Oplus(X3551,X3549,X3548)) = c_Groups_Oplus__class_Oplus(X3551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3551),X3550),X3549),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3551),X3550),X3548)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).
fof(i_0_1684,plain,
! [X3574,X3575,X3576,X3577] :
( ~ class_Rings_Ocomm__semiring__1(X3577)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3577),X3576),c_Groups_Oplus__class_Oplus(X3577,X3575,X3574)) = c_Groups_Oplus__class_Oplus(X3577,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3577),X3576),X3575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3577),X3576),X3574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).
fof(i_0_1685,plain,
! [X5391,X5392,X5393] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5392,X5391)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5393),X5392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5393),X5391))
| X5393 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5393),X5392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5393),X5391))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5392,X5391)
| X5393 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mono])])]) ).
fof(i_0_1686,plain,
! [X5383,X5384,X5385] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5385),X5384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5385),X5383))
| X5385 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5384,X5383) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel])]) ).
fof(i_0_1687,plain,
! [X5374,X5375,X5376] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5376),X5375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5376),X5374))
| X5376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5375,X5374) )
& ( X5376 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5376),X5375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5376),X5374)) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5375,X5374)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5376),X5375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5376),X5374)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj])])]) ).
fof(i_0_1688,plain,
! [X5504,X5505,X5506] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5505),X5506),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5504),X5506))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5505,X5504)
| X5506 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5505,X5504)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5505),X5506),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5504),X5506))
| X5506 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__int])])]) ).
fof(i_0_1689,plain,
! [X5501,X5502,X5503] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5503),X5502),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5501),X5502))
| X5502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5503,X5501) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__int])]) ).
fof(i_0_1690,plain,
! [X5507,X5508,X5509] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5509),X5508),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5507),X5508))
| X5508 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5509,X5507) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__nat])]) ).
fof(i_0_1691,plain,
! [X5433,X5434,X5435] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5434),X5435),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5433),X5435))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5434,X5433)
| X5435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5434,X5433)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5434),X5435),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5433),X5435))
| X5435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__nat])])]) ).
fof(i_0_1692,plain,
! [X4324,X4325,X4326] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4326)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4326),X4325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4326),X4324)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4325,X4324)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4326),X4325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4326),X4324)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4326)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4325,X4324)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4326),X4325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4326),X4324)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_1693,plain,
! [X4327,X4328,X4329] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4328)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4329),X4328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4327),X4328)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4329,X4327)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4329),X4328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4327),X4328)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4328)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4329,X4327)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4329),X4328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4327),X4328)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
fof(i_0_1694,plain,
! [X5702,X5703] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5702,X5703)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5703,X5702))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5703) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5702)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5703,X5702))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5703) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5702,X5703)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5702)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5703,X5702))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5703) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).
fof(i_0_1695,plain,
! [X4242,X4243,X4244] :
( ~ class_Rings_Olinordered__semiring__strict(X4244)
| ~ c_Orderings_Oord__class_Oless(X4244,c_Groups_Ozero__class_Ozero(X4244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4244),X4243),X4242))
| ~ c_Orderings_Oord__class_Oless(X4244,c_Groups_Ozero__class_Ozero(X4244),X4242)
| c_Orderings_Oord__class_Oless(X4244,c_Groups_Ozero__class_Ozero(X4244),X4243) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_1696,plain,
! [X4239,X4240,X4241] :
( ~ class_Rings_Olinordered__semiring__strict(X4241)
| ~ c_Orderings_Oord__class_Oless(X4241,c_Groups_Ozero__class_Ozero(X4241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4241),X4240),X4239))
| ~ c_Orderings_Oord__class_Oless(X4241,c_Groups_Ozero__class_Ozero(X4241),X4240)
| c_Orderings_Oord__class_Oless(X4241,c_Groups_Ozero__class_Ozero(X4241),X4239) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
fof(i_0_1697,plain,
! [X4980,X4981,X4982] :
( ~ class_Groups_Omonoid__mult(X4982)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4982),hAPP(hAPP(c_Power_Opower__class_Opower(X4982),X4981),X4980)),X4981) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4982),X4981),hAPP(hAPP(c_Power_Opower__class_Opower(X4982),X4981),X4980)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_1698,plain,
! [X3421,X3422,X3423,X3424] :
( ~ class_Groups_Oab__semigroup__mult(X3424)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3424),X3423),X3422)),X3421) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3424),X3423),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3424),X3422),X3421)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_1699,plain,
! [X3371,X3372,X3373,X3374] :
( ~ class_Rings_Ocomm__semiring__1(X3374)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3374),X3373),X3372)),X3371) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3374),X3373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3374),X3372),X3371)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_1700,plain,
! [X3375,X3376,X3377,X3378] :
( ~ class_Rings_Ocomm__semiring__1(X3378)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3378),X3377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3378),X3376),X3375)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3378),X3377),X3376)),X3375) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).
fof(i_0_1701,plain,
! [X5564,X5565] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5565,X5564)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5565),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X5564)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5565),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X5564))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5565,X5564) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__real__le])]) ).
fof(i_0_1702,plain,
! [X5566,X5567] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5567,X5566)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5567),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5566),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5567),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5566),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5567,X5566) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__real__less])]) ).
fof(i_0_1703,plain,
! [X4926,X4927,X4928,X4929] :
( ~ class_Rings_Ocomm__semiring__1(X4929)
| hAPP(c_Polynomial_Opoly(X4929,c_Polynomial_Omonom(X4929,X4928,X4927)),X4926) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4929),X4928),hAPP(hAPP(c_Power_Opower__class_Opower(X4929),X4926),X4927)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__monom])]) ).
fof(i_0_1704,plain,
! [X3215,X3216,X3217,X3218,X3219] :
( ( X3215 = hAPP(c_Polynomial_Opoly(X3219,X3218),X3217)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3219),X3218,c_Polynomial_Osmult(X3219,X3217,X3216)) != c_Polynomial_OpCons(X3219,X3215,X3216)
| ~ class_Rings_Ocomm__semiring__0(X3219) )
& ( X3216 = c_Polynomial_Osynthetic__div(X3219,X3218,X3217)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3219),X3218,c_Polynomial_Osmult(X3219,X3217,X3216)) != c_Polynomial_OpCons(X3219,X3215,X3216)
| ~ class_Rings_Ocomm__semiring__0(X3219) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique])])]) ).
fof(i_0_1705,plain,
! [X5683,X5684,X5685,X5686] :
( ~ class_Divides_Osemiring__div(X5686)
| ~ c_Rings_Odvd__class_Odvd(X5686,X5685,X5684)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5686),X5683),c_Divides_Odiv__class_Odiv(X5686,X5684,X5685)) = c_Divides_Odiv__class_Odiv(X5686,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5686),X5683),X5684),X5685) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__swap])]) ).
fof(i_0_1706,plain,
! [X5614] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk34_1(X5614),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X5614)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5614) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5614,c_RealDef_Oreal(tc_Nat_Onat,esk34_1(X5614)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5614) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6])])])]) ).
cnf(i_0_1707,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1280]) ).
fof(i_0_1708,plain,
! [X3168,X3169,X3170,X3171] :
( ~ class_Rings_Ocomm__semiring__0(X3171)
| c_Polynomial_Osynthetic__div(X3171,c_Polynomial_OpCons(X3171,X3170,X3169),X3168) = c_Polynomial_OpCons(X3171,hAPP(c_Polynomial_Opoly(X3171,X3169),X3168),c_Polynomial_Osynthetic__div(X3171,X3169,X3168)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__pCons])]) ).
fof(i_0_1709,plain,
! [X3172,X3173,X3174,X3175] :
( ~ class_Rings_Ocomm__semiring__0(X3175)
| hAPP(c_Polynomial_Opoly(X3175,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3175,X3174,X3173)),X3172) = hAPP(c_Polynomial_Opoly(X3175,X3174),c_Groups_Oplus__class_Oplus(X3175,X3173,X3172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__offset__poly])]) ).
cnf(i_0_1710,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),X1) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1281]) ).
fof(i_0_1711,plain,
! [X4997,X4998,X4999,X5000] :
( ~ class_Groups_Omonoid__mult(X5000)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5000),X4999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4998),X4997)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5000),hAPP(hAPP(c_Power_Opower__class_Opower(X5000),X4999),X4998)),X4997) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_1712,plain,
! [X4657,X4658,X4659,X4660] :
( ~ class_Rings_Ocomm__semiring__1(X4660)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4660),hAPP(hAPP(c_Power_Opower__class_Opower(X4660),X4659),X4658)),X4657) = hAPP(hAPP(c_Power_Opower__class_Opower(X4660),X4659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4658),X4657)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).
fof(i_0_1713,plain,
! [X4953,X4954,X4955] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4955,X4954)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4953)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4953),X4955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4953),X4954)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_1714,plain,
! [X4330,X4331,X4332] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4332,X4331)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4330)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4332),X4330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4331),X4330)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_1715,plain,
! [X4333,X4334,X4335] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4335,X4334)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4333)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4333),X4335),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4333),X4334)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_1716,plain,
! [X4864,X4865,X4866] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4866)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4865,X4864)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4866),X4865),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4866),X4864)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2])]) ).
fof(i_0_1717,plain,
! [X4933,X4934] :
( ( X4934 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4933),X4934) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4933),X4934) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4933),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4933),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4934,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__if])]) ).
fof(i_0_1718,plain,
! [X4342,X4343,X4344] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4344,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4343,X4342))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4344,X4342),X4343) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4344,X4342),X4343)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4344,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4343,X4342)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).
fof(i_0_1719,plain,
! [X3260,X3261,X3262] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3262,X3261),X3260)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3262,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3260,X3261)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3262,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3260,X3261))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3262,X3261),X3260) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).
fof(i_0_1720,plain,
! [X3330,X3331,X3332,X3333] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3333,X3332)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3331,X3330)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3333),X3331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3332),X3330)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).
fof(i_0_1721,plain,
! [X3318,X3319,X3320] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3320,X3319)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3319,X3318),X3320) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3319,X3320),X3318) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).
fof(i_0_1722,plain,
! [X3315,X3316,X3317] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3317,X3316)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3316,X3317),X3315) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3316,X3315),X3317) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).
fof(i_0_1723,plain,
! [X3312,X3313,X3314] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3314,X3313)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3312,X3313),X3314) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3312,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3313,X3314)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).
fof(i_0_1724,plain,
! [X3257,X3258,X3259] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3259,X3258)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3257,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3258,X3259)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3257,X3259),X3258) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).
fof(i_0_1725,plain,
! [X3301,X3302,X3303] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3303,X3302)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3301,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3302,X3303)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3301,X3302),X3303) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).
fof(i_0_1726,plain,
! [X5698,X5699] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5698,X5699))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5698)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5699) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5698)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5698,X5699))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5699) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).
fof(i_0_1727,plain,
! [X5711,X5712] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5711,X5712))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5711,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5712,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5711,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5711,X5712))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5712,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff])])]) ).
fof(i_0_1728,plain,
! [X3449,X3450,X3451,X3452] :
( ~ class_Rings_Ocomm__semiring__0(X3452)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3452)),X3451),c_Polynomial_Osmult(X3452,X3450,X3449)) = c_Polynomial_Osmult(X3452,X3450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3452)),X3451),X3449)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__right])]) ).
fof(i_0_1729,plain,
! [X5700,X5701] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5700,X5701))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5701,X5700)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5701) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5701,X5700)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5700,X5701))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5701) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).
fof(i_0_1730,plain,
! [X3469,X3470,X3471,X3472] :
( ~ class_Rings_Ocomm__semiring__0(X3472)
| hAPP(c_Polynomial_Opoly(X3472,c_Polynomial_Osmult(X3472,X3471,X3470)),X3469) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3472),X3471),hAPP(c_Polynomial_Opoly(X3472,X3470),X3469)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__smult])]) ).
fof(i_0_1731,plain,
! [X3831,X3832,X3833] :
( ( c_Orderings_Oord__class_Oless__eq(X3833,X3832,c_Groups_Ozero__class_Ozero(X3833))
| c_Orderings_Oord__class_Oless__eq(X3833,c_Groups_Ozero__class_Ozero(X3833),X3832)
| ~ c_Orderings_Oord__class_Oless__eq(X3833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3833),X3832),X3831),c_Groups_Ozero__class_Ozero(X3833))
| ~ class_Rings_Olinordered__ring__strict(X3833) )
& ( c_Orderings_Oord__class_Oless__eq(X3833,c_Groups_Ozero__class_Ozero(X3833),X3831)
| c_Orderings_Oord__class_Oless__eq(X3833,c_Groups_Ozero__class_Ozero(X3833),X3832)
| ~ c_Orderings_Oord__class_Oless__eq(X3833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3833),X3832),X3831),c_Groups_Ozero__class_Ozero(X3833))
| ~ class_Rings_Olinordered__ring__strict(X3833) )
& ( c_Orderings_Oord__class_Oless__eq(X3833,X3832,c_Groups_Ozero__class_Ozero(X3833))
| c_Orderings_Oord__class_Oless__eq(X3833,X3831,c_Groups_Ozero__class_Ozero(X3833))
| ~ c_Orderings_Oord__class_Oless__eq(X3833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3833),X3832),X3831),c_Groups_Ozero__class_Ozero(X3833))
| ~ class_Rings_Olinordered__ring__strict(X3833) )
& ( c_Orderings_Oord__class_Oless__eq(X3833,c_Groups_Ozero__class_Ozero(X3833),X3831)
| c_Orderings_Oord__class_Oless__eq(X3833,X3831,c_Groups_Ozero__class_Ozero(X3833))
| ~ c_Orderings_Oord__class_Oless__eq(X3833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3833),X3832),X3831),c_Groups_Ozero__class_Ozero(X3833))
| ~ class_Rings_Olinordered__ring__strict(X3833) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3833,c_Groups_Ozero__class_Ozero(X3833),X3832)
| ~ c_Orderings_Oord__class_Oless__eq(X3833,X3831,c_Groups_Ozero__class_Ozero(X3833))
| c_Orderings_Oord__class_Oless__eq(X3833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3833),X3832),X3831),c_Groups_Ozero__class_Ozero(X3833))
| ~ class_Rings_Olinordered__ring__strict(X3833) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3833,X3832,c_Groups_Ozero__class_Ozero(X3833))
| ~ c_Orderings_Oord__class_Oless__eq(X3833,c_Groups_Ozero__class_Ozero(X3833),X3831)
| c_Orderings_Oord__class_Oless__eq(X3833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3833),X3832),X3831),c_Groups_Ozero__class_Ozero(X3833))
| ~ class_Rings_Olinordered__ring__strict(X3833) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
fof(i_0_1732,plain,
! [X3834,X3835,X3836] :
( ( c_Orderings_Oord__class_Oless__eq(X3836,X3835,c_Groups_Ozero__class_Ozero(X3836))
| c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),X3835)
| ~ c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),X3835),X3834))
| ~ class_Rings_Olinordered__ring__strict(X3836) )
& ( c_Orderings_Oord__class_Oless__eq(X3836,X3834,c_Groups_Ozero__class_Ozero(X3836))
| c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),X3835)
| ~ c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),X3835),X3834))
| ~ class_Rings_Olinordered__ring__strict(X3836) )
& ( c_Orderings_Oord__class_Oless__eq(X3836,X3835,c_Groups_Ozero__class_Ozero(X3836))
| c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),X3834)
| ~ c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),X3835),X3834))
| ~ class_Rings_Olinordered__ring__strict(X3836) )
& ( c_Orderings_Oord__class_Oless__eq(X3836,X3834,c_Groups_Ozero__class_Ozero(X3836))
| c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),X3834)
| ~ c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),X3835),X3834))
| ~ class_Rings_Olinordered__ring__strict(X3836) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),X3835)
| ~ c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),X3834)
| c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),X3835),X3834))
| ~ class_Rings_Olinordered__ring__strict(X3836) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3836,X3835,c_Groups_Ozero__class_Ozero(X3836))
| ~ c_Orderings_Oord__class_Oless__eq(X3836,X3834,c_Groups_Ozero__class_Ozero(X3836))
| c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Ozero__class_Ozero(X3836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),X3835),X3834))
| ~ class_Rings_Olinordered__ring__strict(X3836) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).
fof(i_0_1733,plain,
! [X5380,X5381,X5382] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5382,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5381,X5380))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5382,X5380)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5382,X5381) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zdiffD])]) ).
fof(i_0_1734,plain,
! [X4972,X4973,X4974] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4974),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4973,X4972)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4974),X4973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4974),X4972)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(i_0_1735,plain,
! [X4960,X4961,X4962] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4962),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4961,X4960)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4962),X4961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4962),X4960)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_1736,plain,
! [X3735,X3736,X3737] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3737),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3736,X3735)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3737),X3736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3737),X3735)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(i_0_1737,plain,
! [X3705,X3706,X3707] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3707),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3706,X3705)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3707),X3706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3707),X3705)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
fof(i_0_1738,plain,
! [X3873,X3874,X3875,X3876] :
( ~ class_Rings_Ocomm__semiring__0(X3876)
| hAPP(c_Polynomial_Opoly(X3876,c_Polynomial_Opcompose(X3876,X3875,X3874)),X3873) = hAPP(c_Polynomial_Opoly(X3876,X3875),hAPP(c_Polynomial_Opoly(X3876,X3874),X3873)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pcompose])]) ).
fof(i_0_1739,plain,
! [X4306,X4307] :
( ~ class_Rings_Ocomm__semiring__1(X4307)
| c_Groups_Oplus__class_Oplus(X4307,X4306,X4306) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4307),c_Groups_Oplus__class_Oplus(X4307,c_Groups_Oone__class_Oone(X4307),c_Groups_Oone__class_Oone(X4307))),X4306) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).
fof(i_0_1740,plain,
! [X3627,X3628] :
( ( X3628 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3628),X3628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3627),X3627)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3627 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3628),X3628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3627),X3627)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3628 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3627 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3628),X3628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3627),X3627)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__two__squares__add__zero__iff])])]) ).
cnf(i_0_1741,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_1282]) ).
cnf(i_0_1742,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(split_conjunct,[status(thm)],[i_0_1283]) ).
cnf(i_0_1743,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = c_Nat_OSuc(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1284]) ).
cnf(i_0_1744,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = c_Nat_OSuc(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1285]) ).
fof(i_0_1745,plain,
! [X4282,X4283,X4284] :
( ~ class_Groups_Oordered__comm__monoid__add(X4284)
| ~ c_Orderings_Oord__class_Oless(X4284,X4283,c_Groups_Ozero__class_Ozero(X4284))
| ~ c_Orderings_Oord__class_Oless(X4284,X4282,c_Groups_Ozero__class_Ozero(X4284))
| c_Orderings_Oord__class_Oless(X4284,c_Groups_Oplus__class_Oplus(X4284,X4283,X4282),c_Groups_Ozero__class_Ozero(X4284)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_1746,plain,
! [X4405,X4406,X4407] :
( ~ class_Groups_Oordered__comm__monoid__add(X4407)
| ~ c_Orderings_Oord__class_Oless__eq(X4407,X4406,c_Groups_Ozero__class_Ozero(X4407))
| ~ c_Orderings_Oord__class_Oless(X4407,X4405,c_Groups_Ozero__class_Ozero(X4407))
| c_Orderings_Oord__class_Oless(X4407,c_Groups_Oplus__class_Oplus(X4407,X4406,X4405),c_Groups_Ozero__class_Ozero(X4407)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_1747,plain,
! [X4408,X4409,X4410] :
( ~ class_Groups_Oordered__comm__monoid__add(X4410)
| ~ c_Orderings_Oord__class_Oless(X4410,X4409,c_Groups_Ozero__class_Ozero(X4410))
| ~ c_Orderings_Oord__class_Oless__eq(X4410,X4408,c_Groups_Ozero__class_Ozero(X4410))
| c_Orderings_Oord__class_Oless(X4410,c_Groups_Oplus__class_Oplus(X4410,X4409,X4408),c_Groups_Ozero__class_Ozero(X4410)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_1748,plain,
! [X3001,X3002,X3003] :
( ~ class_Groups_Oordered__comm__monoid__add(X3003)
| ~ c_Orderings_Oord__class_Oless__eq(X3003,X3002,c_Groups_Ozero__class_Ozero(X3003))
| ~ c_Orderings_Oord__class_Oless__eq(X3003,X3001,c_Groups_Ozero__class_Ozero(X3003))
| c_Orderings_Oord__class_Oless__eq(X3003,c_Groups_Oplus__class_Oplus(X3003,X3002,X3001),c_Groups_Ozero__class_Ozero(X3003)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_1749,plain,
! [X4279,X4280,X4281] :
( ~ class_Groups_Oordered__comm__monoid__add(X4281)
| ~ c_Orderings_Oord__class_Oless(X4281,c_Groups_Ozero__class_Ozero(X4281),X4280)
| ~ c_Orderings_Oord__class_Oless(X4281,c_Groups_Ozero__class_Ozero(X4281),X4279)
| c_Orderings_Oord__class_Oless(X4281,c_Groups_Ozero__class_Ozero(X4281),c_Groups_Oplus__class_Oplus(X4281,X4280,X4279)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_1750,plain,
! [X4419,X4420,X4421] :
( ~ class_Groups_Oordered__comm__monoid__add(X4421)
| ~ c_Orderings_Oord__class_Oless__eq(X4421,c_Groups_Ozero__class_Ozero(X4421),X4420)
| ~ c_Orderings_Oord__class_Oless(X4421,c_Groups_Ozero__class_Ozero(X4421),X4419)
| c_Orderings_Oord__class_Oless(X4421,c_Groups_Ozero__class_Ozero(X4421),c_Groups_Oplus__class_Oplus(X4421,X4420,X4419)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_1751,plain,
! [X4422,X4423,X4424] :
( ~ class_Groups_Oordered__comm__monoid__add(X4424)
| ~ c_Orderings_Oord__class_Oless(X4424,c_Groups_Ozero__class_Ozero(X4424),X4423)
| ~ c_Orderings_Oord__class_Oless__eq(X4424,c_Groups_Ozero__class_Ozero(X4424),X4422)
| c_Orderings_Oord__class_Oless(X4424,c_Groups_Ozero__class_Ozero(X4424),c_Groups_Oplus__class_Oplus(X4424,X4423,X4422)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_1752,plain,
! [X3015,X3016,X3017] :
( ~ class_Groups_Oordered__comm__monoid__add(X3017)
| ~ c_Orderings_Oord__class_Oless__eq(X3017,c_Groups_Ozero__class_Ozero(X3017),X3016)
| ~ c_Orderings_Oord__class_Oless__eq(X3017,c_Groups_Ozero__class_Ozero(X3017),X3015)
| c_Orderings_Oord__class_Oless__eq(X3017,c_Groups_Ozero__class_Ozero(X3017),c_Groups_Oplus__class_Oplus(X3017,X3016,X3015)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_1753,plain,
! [X5625,X5626,X5628] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk37_2(X5625,X5626))
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5628),X5626)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X5625),X5628)),esk37_2(X5625,X5626)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__bound__exists])])])]) ).
fof(i_0_1754,plain,
! [X4314,X4315] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4315,X4314))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4315)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4314) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4315)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4315,X4314)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4314)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4315,X4314)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_1755,plain,
! [X4661,X4662,X4663] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4663),X4662)),X4661) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4662),X4661)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_1756,plain,
! [X4969,X4970,X4971] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4971),X4970)),X4969) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4970),X4969)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_1757,plain,
! [X3738,X3739,X3740] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3740),X3739)),X3738) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3739),X3738)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_1758,plain,
! [X3747,X3748,X3749] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3749),X3748)),X3747) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3748),X3747)),
inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).
fof(i_0_1759,plain,
! [X4249,X4250,X4251] :
( ~ class_Rings_Olinordered__semiring__strict(X4251)
| ~ c_Orderings_Oord__class_Oless(X4251,X4250,c_Groups_Ozero__class_Ozero(X4251))
| ~ c_Orderings_Oord__class_Oless(X4251,c_Groups_Ozero__class_Ozero(X4251),X4249)
| c_Orderings_Oord__class_Oless(X4251,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4251),X4250),X4249),c_Groups_Ozero__class_Ozero(X4251)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_1760,plain,
! [X4233,X4234,X4235] :
( ~ class_Rings_Olinordered__semiring__strict(X4235)
| ~ c_Orderings_Oord__class_Oless(X4235,c_Groups_Ozero__class_Ozero(X4235),X4234)
| ~ c_Orderings_Oord__class_Oless(X4235,X4233,c_Groups_Ozero__class_Ozero(X4235))
| c_Orderings_Oord__class_Oless(X4235,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4235),X4234),X4233),c_Groups_Ozero__class_Ozero(X4235)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_1761,plain,
! [X4236,X4237,X4238] :
( ~ class_Rings_Olinordered__semiring__strict(X4238)
| ~ c_Orderings_Oord__class_Oless(X4238,c_Groups_Ozero__class_Ozero(X4238),X4237)
| ~ c_Orderings_Oord__class_Oless(X4238,X4236,c_Groups_Ozero__class_Ozero(X4238))
| c_Orderings_Oord__class_Oless(X4238,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4238),X4236),X4237),c_Groups_Ozero__class_Ozero(X4238)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_1762,plain,
! [X3819,X3820,X3821] :
( ~ class_Rings_Oordered__cancel__semiring(X3821)
| ~ c_Orderings_Oord__class_Oless__eq(X3821,X3820,c_Groups_Ozero__class_Ozero(X3821))
| ~ c_Orderings_Oord__class_Oless__eq(X3821,c_Groups_Ozero__class_Ozero(X3821),X3819)
| c_Orderings_Oord__class_Oless__eq(X3821,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3821),X3820),X3819),c_Groups_Ozero__class_Ozero(X3821)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).
fof(i_0_1763,plain,
! [X3780,X3781,X3782] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3782,c_Groups_Ozero__class_Ozero(X3782),X3781)
| ~ c_Orderings_Oord__class_Oless__eq(X3782,X3780,c_Groups_Ozero__class_Ozero(X3782))
| c_Orderings_Oord__class_Oless__eq(X3782,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3782),X3781),X3780),c_Groups_Ozero__class_Ozero(X3782))
| ~ class_Rings_Oordered__cancel__semiring(X3782) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3782,X3781,c_Groups_Ozero__class_Ozero(X3782))
| ~ c_Orderings_Oord__class_Oless__eq(X3782,c_Groups_Ozero__class_Ozero(X3782),X3780)
| c_Orderings_Oord__class_Oless__eq(X3782,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3782),X3781),X3780),c_Groups_Ozero__class_Ozero(X3782))
| ~ class_Rings_Oordered__cancel__semiring(X3782) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).
fof(i_0_1764,plain,
! [X3825,X3826,X3827] :
( ~ class_Rings_Oordered__cancel__semiring(X3827)
| ~ c_Orderings_Oord__class_Oless__eq(X3827,c_Groups_Ozero__class_Ozero(X3827),X3826)
| ~ c_Orderings_Oord__class_Oless__eq(X3827,X3825,c_Groups_Ozero__class_Ozero(X3827))
| c_Orderings_Oord__class_Oless__eq(X3827,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3827),X3826),X3825),c_Groups_Ozero__class_Ozero(X3827)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).
fof(i_0_1765,plain,
! [X3822,X3823,X3824] :
( ~ class_Rings_Oordered__cancel__semiring(X3824)
| ~ c_Orderings_Oord__class_Oless__eq(X3824,c_Groups_Ozero__class_Ozero(X3824),X3823)
| ~ c_Orderings_Oord__class_Oless__eq(X3824,X3822,c_Groups_Ozero__class_Ozero(X3824))
| c_Orderings_Oord__class_Oless__eq(X3824,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3824),X3822),X3823),c_Groups_Ozero__class_Ozero(X3824)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).
fof(i_0_1766,plain,
! [X3932,X3933,X3934] :
( ~ class_Rings_Olinordered__semidom(X3934)
| ~ c_Orderings_Oord__class_Oless(X3934,c_Groups_Oone__class_Oone(X3934),X3933)
| ~ c_Orderings_Oord__class_Oless(X3934,c_Groups_Oone__class_Oone(X3934),X3932)
| c_Orderings_Oord__class_Oless(X3934,c_Groups_Oone__class_Oone(X3934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3934),X3933),X3932)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_1767,plain,
! [X4230,X4231,X4232] :
( ~ class_Rings_Olinordered__semiring__strict(X4232)
| ~ c_Orderings_Oord__class_Oless(X4232,c_Groups_Ozero__class_Ozero(X4232),X4231)
| ~ c_Orderings_Oord__class_Oless(X4232,c_Groups_Ozero__class_Ozero(X4232),X4230)
| c_Orderings_Oord__class_Oless(X4232,c_Groups_Ozero__class_Ozero(X4232),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4232),X4231),X4230)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_1768,plain,
! [X3828,X3829,X3830] :
( ~ class_Rings_Oordered__cancel__semiring(X3830)
| ~ c_Orderings_Oord__class_Oless__eq(X3830,c_Groups_Ozero__class_Ozero(X3830),X3829)
| ~ c_Orderings_Oord__class_Oless__eq(X3830,c_Groups_Ozero__class_Ozero(X3830),X3828)
| c_Orderings_Oord__class_Oless__eq(X3830,c_Groups_Ozero__class_Ozero(X3830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3830),X3829),X3828)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).
fof(i_0_1769,plain,
! [X3783,X3784,X3785] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3785,c_Groups_Ozero__class_Ozero(X3785),X3784)
| ~ c_Orderings_Oord__class_Oless__eq(X3785,c_Groups_Ozero__class_Ozero(X3785),X3783)
| c_Orderings_Oord__class_Oless__eq(X3785,c_Groups_Ozero__class_Ozero(X3785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3785),X3784),X3783))
| ~ class_Rings_Oordered__ring(X3785) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3785,X3784,c_Groups_Ozero__class_Ozero(X3785))
| ~ c_Orderings_Oord__class_Oless__eq(X3785,X3783,c_Groups_Ozero__class_Ozero(X3785))
| c_Orderings_Oord__class_Oless__eq(X3785,c_Groups_Ozero__class_Ozero(X3785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3785),X3784),X3783))
| ~ class_Rings_Oordered__ring(X3785) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).
fof(i_0_1770,plain,
! [X4252,X4253,X4254] :
( ~ class_Rings_Olinordered__ring__strict(X4254)
| ~ c_Orderings_Oord__class_Oless(X4254,X4253,c_Groups_Ozero__class_Ozero(X4254))
| ~ c_Orderings_Oord__class_Oless(X4254,X4252,c_Groups_Ozero__class_Ozero(X4254))
| c_Orderings_Oord__class_Oless(X4254,c_Groups_Ozero__class_Ozero(X4254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4254),X4253),X4252)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_1771,plain,
! [X3816,X3817,X3818] :
( ~ class_Rings_Oordered__ring(X3818)
| ~ c_Orderings_Oord__class_Oless__eq(X3818,X3817,c_Groups_Ozero__class_Ozero(X3818))
| ~ c_Orderings_Oord__class_Oless__eq(X3818,X3816,c_Groups_Ozero__class_Ozero(X3818))
| c_Orderings_Oord__class_Oless__eq(X3818,c_Groups_Ozero__class_Ozero(X3818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3818),X3817),X3816)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).
fof(i_0_1772,plain,
! [X4116,X4117,X4118,X4119] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4119)
| ~ c_Orderings_Oord__class_Oless(X4119,X4118,X4117)
| c_Orderings_Oord__class_Oless(X4119,c_Groups_Oplus__class_Oplus(X4119,X4118,X4116),c_Groups_Oplus__class_Oplus(X4119,X4117,X4116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_1773,plain,
! [X4112,X4113,X4114,X4115] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4115)
| ~ c_Orderings_Oord__class_Oless(X4115,X4114,X4113)
| c_Orderings_Oord__class_Oless(X4115,c_Groups_Oplus__class_Oplus(X4115,X4112,X4114),c_Groups_Oplus__class_Oplus(X4115,X4112,X4113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_1774,plain,
! [X2959,X2960,X2961,X2962] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2962)
| ~ c_Orderings_Oord__class_Oless__eq(X2962,X2961,X2960)
| c_Orderings_Oord__class_Oless__eq(X2962,c_Groups_Oplus__class_Oplus(X2962,X2961,X2959),c_Groups_Oplus__class_Oplus(X2962,X2960,X2959)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_1775,plain,
! [X2963,X2964,X2965,X2966] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2966)
| ~ c_Orderings_Oord__class_Oless__eq(X2966,X2965,X2964)
| c_Orderings_Oord__class_Oless__eq(X2966,c_Groups_Oplus__class_Oplus(X2966,X2963,X2965),c_Groups_Oplus__class_Oplus(X2966,X2963,X2964)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_1776,plain,
! [X5680,X5681,X5682] :
( ~ class_Divides_Osemiring__div(X5682)
| ~ c_Rings_Odvd__class_Odvd(X5682,X5681,X5680)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5682),c_Divides_Odiv__class_Odiv(X5682,X5680,X5681)),X5681) = X5680 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult__self])]) ).
fof(i_0_1777,plain,
! [X5492,X5493,X5494] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5494,X5492)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5493,X5492)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5492,X5493)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5494,X5493)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5493,X5494) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5492,X5494)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5493,X5492)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5492,X5493)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5494,X5493)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5493,X5494) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1286])])]) ).
cnf(i_0_1778,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1272]) ).
cnf(i_0_1779,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1287]) ).
cnf(i_0_1780,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1273]) ).
fof(i_0_1781,plain,
! [X4948,X4949,X4950] :
( ~ class_Rings_Olinordered__semidom(X4950)
| ~ c_Orderings_Oord__class_Oless(X4950,c_Groups_Oone__class_Oone(X4950),X4949)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4948)
| c_Orderings_Oord__class_Oless(X4950,c_Groups_Oone__class_Oone(X4950),hAPP(hAPP(c_Power_Opower__class_Opower(X4950),X4949),X4948)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
fof(i_0_1782,plain,
! [X5243,X5244,X5245,X5246] :
( ~ class_Rings_Ocomm__semiring__1(X5246)
| ~ c_Rings_Odvd__class_Odvd(X5246,X5245,X5244)
| c_Rings_Odvd__class_Odvd(X5246,hAPP(hAPP(c_Power_Opower__class_Opower(X5246),X5245),X5243),hAPP(hAPP(c_Power_Opower__class_Opower(X5246),X5244),X5243)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__same])]) ).
fof(i_0_1783,plain,
! [X5586,X5587] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5587),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5586)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5587,c_RealDef_Oreal(tc_Nat_Onat,X5586)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt])]) ).
fof(i_0_1784,plain,
! [X4287,X4288,X4289,X4290] :
( ~ class_Rings_Olinordered__semidom(X4290)
| ~ c_Orderings_Oord__class_Oless(X4290,c_Groups_Ozero__class_Ozero(X4290),X4289)
| ~ c_Orderings_Oord__class_Oless(X4290,X4288,X4287)
| c_Orderings_Oord__class_Oless(X4290,X4288,c_Groups_Oplus__class_Oplus(X4290,X4289,X4287)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_1785,plain,
! [X4411,X4412,X4413,X4414] :
( ~ class_Groups_Oordered__comm__monoid__add(X4414)
| ~ c_Orderings_Oord__class_Oless__eq(X4414,c_Groups_Ozero__class_Ozero(X4414),X4413)
| ~ c_Orderings_Oord__class_Oless(X4414,X4412,X4411)
| c_Orderings_Oord__class_Oless(X4414,X4412,c_Groups_Oplus__class_Oplus(X4414,X4413,X4411)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_1786,plain,
! [X4415,X4416,X4417,X4418] :
( ~ class_Groups_Oordered__comm__monoid__add(X4418)
| ~ c_Orderings_Oord__class_Oless(X4418,c_Groups_Ozero__class_Ozero(X4418),X4417)
| ~ c_Orderings_Oord__class_Oless__eq(X4418,X4416,X4415)
| c_Orderings_Oord__class_Oless(X4418,X4416,c_Groups_Oplus__class_Oplus(X4418,X4417,X4415)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_1787,plain,
! [X3008,X3009,X3010,X3011] :
( ~ class_Groups_Oordered__comm__monoid__add(X3011)
| ~ c_Orderings_Oord__class_Oless__eq(X3011,c_Groups_Ozero__class_Ozero(X3011),X3010)
| ~ c_Orderings_Oord__class_Oless__eq(X3011,X3009,X3008)
| c_Orderings_Oord__class_Oless__eq(X3011,X3009,c_Groups_Oplus__class_Oplus(X3011,X3010,X3008)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_1788,plain,
! [X3004,X3005,X3006,X3007] :
( ~ class_Groups_Oordered__comm__monoid__add(X3007)
| ~ c_Orderings_Oord__class_Oless__eq(X3007,c_Groups_Ozero__class_Ozero(X3007),X3006)
| ~ c_Orderings_Oord__class_Oless__eq(X3007,X3005,X3004)
| c_Orderings_Oord__class_Oless__eq(X3007,X3005,c_Groups_Oplus__class_Oplus(X3007,X3004,X3006)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_1789,plain,
! [X5239,X5240,X5241,X5242] :
( ~ class_Rings_Ocomm__semiring__1(X5242)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5241,X5240)
| c_Rings_Odvd__class_Odvd(X5242,hAPP(hAPP(c_Power_Opower__class_Opower(X5242),X5239),X5241),hAPP(hAPP(c_Power_Opower__class_Opower(X5242),X5239),X5240)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd])]) ).
fof(i_0_1790,plain,
! [X5363,X5364] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5364)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5363)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5364,X5363)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5363,X5364)
| X5364 = X5363 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__nonneg])]) ).
fof(i_0_1791,plain,
! [X4792,X4793] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4793),X4793)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4792),X4792)),
inference(variable_rename,[status(thm)],[fact_real__minus__mult__self__le]) ).
fof(i_0_1792,plain,
! [X5126,X5127,X5128] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5128,X5127)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5128,X5126),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5127,X5126)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_1793,plain,
! [X4162,X4163,X4164] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4164,X4163)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4164,X4162),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4163,X4162)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_1794,plain,
! [X5145,X5146,X5147] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5147,X5146)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5145,X5147),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5145,X5146)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).
fof(i_0_1795,plain,
! [X3294,X3295,X3296] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3296,X3295)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3296,X3294),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3295,X3294)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).
fof(i_0_1796,plain,
! [X3291,X3292,X3293] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3293,X3292)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3291,X3292),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3291,X3293)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).
fof(i_0_1797,plain,
! [X3282,X3283,X3284] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3284,X3283)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3284,X3282),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3283,X3282)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_1798,plain,
! [X2948,X2949,X2950] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2950,X2949)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2948,X2950),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2948,X2949)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).
cnf(i_0_1799,plain,
( X1 = c_Nat_OSuc(esk17_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1288]) ).
cnf(i_0_1800,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1289]) ).
fof(i_0_1801,plain,
! [X5320,X5321,X5322,X5323] :
( ~ class_Rings_Ocomm__ring__1(X5323)
| ~ c_Rings_Odvd__class_Odvd(X5323,X5322,X5321)
| ~ c_Rings_Odvd__class_Odvd(X5323,X5322,X5320)
| c_Rings_Odvd__class_Odvd(X5323,X5322,c_Groups_Ominus__class_Ominus(X5323,X5321,X5320)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff])]) ).
fof(i_0_1802,plain,
! [X5294,X5295,X5296,X5297] :
( ~ class_Rings_Ocomm__semiring__1(X5297)
| ~ c_Rings_Odvd__class_Odvd(X5297,X5296,X5295)
| ~ c_Rings_Odvd__class_Odvd(X5297,X5296,X5294)
| c_Rings_Odvd__class_Odvd(X5297,X5296,c_Groups_Oplus__class_Oplus(X5297,X5295,X5294)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__add])]) ).
fof(i_0_1803,plain,
! [X5645,X5646,X5647] :
( ~ class_Divides_Osemiring__div(X5647)
| X5646 = c_Groups_Ozero__class_Ozero(X5647)
| c_Divides_Odiv__class_Odiv(X5647,c_Groups_Oplus__class_Oplus(X5647,X5646,X5645),X5646) = c_Groups_Oplus__class_Oplus(X5647,c_Divides_Odiv__class_Odiv(X5647,X5645,X5646),c_Groups_Oone__class_Oone(X5647)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).
fof(i_0_1804,plain,
! [X5642,X5643,X5644] :
( ~ class_Divides_Osemiring__div(X5644)
| X5643 = c_Groups_Ozero__class_Ozero(X5644)
| c_Divides_Odiv__class_Odiv(X5644,c_Groups_Oplus__class_Oplus(X5644,X5642,X5643),X5643) = c_Groups_Oplus__class_Oplus(X5644,c_Divides_Odiv__class_Odiv(X5644,X5642,X5643),c_Groups_Oone__class_Oone(X5644)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).
cnf(i_0_1805,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1290]) ).
cnf(i_0_1806,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1291]) ).
cnf(i_0_1807,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk17_2(X1,X2),X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1288]) ).
cnf(i_0_1808,plain,
( c_Polynomial_Omonom(X1,X2,c_Nat_OSuc(X3)) = c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),c_Polynomial_Omonom(X1,X2,X3))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1292]) ).
fof(i_0_1809,plain,
! [X5707,X5708] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5708)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5707,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5708,X5707),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0])]) ).
fof(i_0_1810,plain,
! [X5713,X5714] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5714,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5713)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5714,X5713),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0])]) ).
fof(i_0_1811,plain,
! [X5205,X5206] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5206)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5205)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5206,X5205)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_1812,plain,
! [X5331,X5332,X5333,X5334] :
( ( X5333 != c_Groups_Ozero__class_Ozero(X5334)
| X5331 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5334))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5334),c_Polynomial_Osmult(X5334,X5333,X5332),X5331)
| ~ class_Fields_Ofield(X5334) )
& ( X5333 = c_Groups_Ozero__class_Ozero(X5334)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5334),X5332,X5331)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5334),c_Polynomial_Osmult(X5334,X5333,X5332),X5331)
| ~ class_Fields_Ofield(X5334) )
& ( X5333 != c_Groups_Ozero__class_Ozero(X5334)
| X5333 = c_Groups_Ozero__class_Ozero(X5334)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5334),c_Polynomial_Osmult(X5334,X5333,X5332),X5331)
| ~ class_Fields_Ofield(X5334) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5334),X5332,X5331)
| X5333 = c_Groups_Ozero__class_Ozero(X5334)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5334),c_Polynomial_Osmult(X5334,X5333,X5332),X5331)
| ~ class_Fields_Ofield(X5334) )
& ( X5333 != c_Groups_Ozero__class_Ozero(X5334)
| X5331 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5334))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5334),c_Polynomial_Osmult(X5334,X5333,X5332),X5331)
| ~ class_Fields_Ofield(X5334) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5334),X5332,X5331)
| X5331 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5334))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5334),c_Polynomial_Osmult(X5334,X5333,X5332),X5331)
| ~ class_Fields_Ofield(X5334) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd__iff])])]) ).
fof(i_0_1813,plain,
! [X5308,X5309,X5310,X5311] :
( ~ class_Fields_Ofield(X5311)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5311),X5310,c_Polynomial_Osmult(X5311,X5309,X5308))
| X5309 = c_Groups_Ozero__class_Ozero(X5311)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5311),X5310,X5308) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__smult__cancel])]) ).
fof(i_0_1814,plain,
! [X5300,X5301,X5302,X5303] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5303),X5301,c_Polynomial_Osmult(X5303,X5302,X5300))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5303),X5301,X5300)
| X5302 = c_Groups_Ozero__class_Ozero(X5303)
| ~ class_Fields_Ofield(X5303) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5303),X5301,X5300)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5303),X5301,c_Polynomial_Osmult(X5303,X5302,X5300))
| X5302 = c_Groups_Ozero__class_Ozero(X5303)
| ~ class_Fields_Ofield(X5303) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__smult__iff])])]) ).
cnf(i_0_1815,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_1293]) ).
cnf(i_0_1816,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X3))
| X1 != c_Nat_OSuc(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1288]) ).
fof(i_0_1817,plain,
! [X3334,X3335,X3336] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3335,X3336) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3334,X3336)
| X3335 = X3334
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3336,X3334)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3336,X3335) )
& ( X3335 != X3334
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3335,X3336) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3334,X3336)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3336,X3334)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3336,X3335) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).
fof(i_0_1818,plain,
! [X5726,X5727] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5727)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5726)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5727,X5726),X5727) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).
fof(i_0_1819,plain,
! [X4338,X4339] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4339)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4338)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4338,X4339),X4338) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).
fof(i_0_1820,plain,
! [X5576,X5577] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5577),X5576)
| c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5576,c_RealDef_Oreal(tc_Nat_Onat,X5577))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X5576),X5577) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__subtract])]) ).
fof(i_0_1821,plain,
! [X5573,X5574] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5574),X5573)
| c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5573,c_RealDef_Oreal(tc_Nat_Onat,X5574))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X5573),X5574) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__subtract])]) ).
fof(i_0_1822,plain,
! [X5284,X5285,X5286,X5287] :
( ~ class_Rings_Ocomm__semiring__1(X5287)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5287),c_Polynomial_Osmult(X5287,X5286,X5285),X5284)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5287),X5285,X5284) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd__cancel])]) ).
fof(i_0_1823,plain,
! [X4275,X4276] :
( ( ~ c_Orderings_Oord__class_Oless(X4276,c_Groups_Ozero__class_Ozero(X4276),c_Groups_Oplus__class_Oplus(X4276,X4275,X4275))
| c_Orderings_Oord__class_Oless(X4276,c_Groups_Ozero__class_Ozero(X4276),X4275)
| ~ class_Groups_Olinordered__ab__group__add(X4276) )
& ( ~ c_Orderings_Oord__class_Oless(X4276,c_Groups_Ozero__class_Ozero(X4276),X4275)
| c_Orderings_Oord__class_Oless(X4276,c_Groups_Ozero__class_Ozero(X4276),c_Groups_Oplus__class_Oplus(X4276,X4275,X4275))
| ~ class_Groups_Olinordered__ab__group__add(X4276) ) ),
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_1824,plain,
! [X3020,X3021] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),c_Groups_Oplus__class_Oplus(X3021,X3020,X3020))
| c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),X3020)
| ~ class_Groups_Olinordered__ab__group__add(X3021) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),X3020)
| c_Orderings_Oord__class_Oless__eq(X3021,c_Groups_Ozero__class_Ozero(X3021),c_Groups_Oplus__class_Oplus(X3021,X3020,X3020))
| ~ class_Groups_Olinordered__ab__group__add(X3021) ) ),
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_1825,plain,
! [X4285,X4286] :
( ( ~ c_Orderings_Oord__class_Oless(X4286,c_Groups_Oplus__class_Oplus(X4286,X4285,X4285),c_Groups_Ozero__class_Ozero(X4286))
| c_Orderings_Oord__class_Oless(X4286,X4285,c_Groups_Ozero__class_Ozero(X4286))
| ~ class_Rings_Olinordered__idom(X4286) )
& ( ~ c_Orderings_Oord__class_Oless(X4286,X4285,c_Groups_Ozero__class_Ozero(X4286))
| c_Orderings_Oord__class_Oless(X4286,c_Groups_Oplus__class_Oplus(X4286,X4285,X4285),c_Groups_Ozero__class_Ozero(X4286))
| ~ class_Rings_Olinordered__idom(X4286) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_1826,plain,
! [X4277,X4278] :
( ( ~ c_Orderings_Oord__class_Oless(X4278,c_Groups_Oplus__class_Oplus(X4278,X4277,X4277),c_Groups_Ozero__class_Ozero(X4278))
| c_Orderings_Oord__class_Oless(X4278,X4277,c_Groups_Ozero__class_Ozero(X4278))
| ~ class_Groups_Olinordered__ab__group__add(X4278) )
& ( ~ c_Orderings_Oord__class_Oless(X4278,X4277,c_Groups_Ozero__class_Ozero(X4278))
| c_Orderings_Oord__class_Oless(X4278,c_Groups_Oplus__class_Oplus(X4278,X4277,X4277),c_Groups_Ozero__class_Ozero(X4278))
| ~ class_Groups_Olinordered__ab__group__add(X4278) ) ),
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_1827,plain,
! [X3018,X3019] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3019,c_Groups_Oplus__class_Oplus(X3019,X3018,X3018),c_Groups_Ozero__class_Ozero(X3019))
| c_Orderings_Oord__class_Oless__eq(X3019,X3018,c_Groups_Ozero__class_Ozero(X3019))
| ~ class_Groups_Olinordered__ab__group__add(X3019) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3019,X3018,c_Groups_Ozero__class_Ozero(X3019))
| c_Orderings_Oord__class_Oless__eq(X3019,c_Groups_Oplus__class_Oplus(X3019,X3018,X3018),c_Groups_Ozero__class_Ozero(X3019))
| ~ class_Groups_Olinordered__ab__group__add(X3019) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])]) ).
cnf(i_0_1828,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_1294]) ).
fof(i_0_1829,plain,
! [X3200,X3201,X3202,X3203] :
( ~ class_Rings_Ocomm__semiring__1(X3203)
| c_Groups_Oplus__class_Oplus(X3203,c_Groups_Oplus__class_Oplus(X3203,X3202,X3201),X3200) = c_Groups_Oplus__class_Oplus(X3203,c_Groups_Oplus__class_Oplus(X3203,X3202,X3200),X3201) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_1830,plain,
! [X3196,X3197,X3198,X3199] :
( ~ class_Rings_Ocomm__semiring__1(X3199)
| c_Groups_Oplus__class_Oplus(X3199,c_Groups_Oplus__class_Oplus(X3199,X3198,X3197),X3196) = c_Groups_Oplus__class_Oplus(X3199,X3198,c_Groups_Oplus__class_Oplus(X3199,X3197,X3196)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_1831,plain,
! [X3105,X3106,X3107,X3108] :
( ~ class_Groups_Oab__semigroup__add(X3108)
| c_Groups_Oplus__class_Oplus(X3108,c_Groups_Oplus__class_Oplus(X3108,X3107,X3106),X3105) = c_Groups_Oplus__class_Oplus(X3108,X3107,c_Groups_Oplus__class_Oplus(X3108,X3106,X3105)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_1832,plain,
! [X3192,X3193,X3194,X3195] :
( ~ class_Rings_Ocomm__semiring__1(X3195)
| c_Groups_Oplus__class_Oplus(X3195,X3194,c_Groups_Oplus__class_Oplus(X3195,X3193,X3192)) = c_Groups_Oplus__class_Oplus(X3195,c_Groups_Oplus__class_Oplus(X3195,X3194,X3193),X3192) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_1833,plain,
! [X3188,X3189,X3190,X3191] :
( ~ class_Rings_Ocomm__semiring__1(X3191)
| c_Groups_Oplus__class_Oplus(X3191,X3190,c_Groups_Oplus__class_Oplus(X3191,X3189,X3188)) = c_Groups_Oplus__class_Oplus(X3191,X3189,c_Groups_Oplus__class_Oplus(X3191,X3190,X3188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_1834,plain,
! [X4562,X4563] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4563,X4562))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4563),X4562) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4563),X4562)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4563,X4562)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])]) ).
fof(i_0_1835,plain,
! [X4887,X4888] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4888,X4887))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4888),X4887) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4888),X4887)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4888,X4887)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff])]) ).
fof(i_0_1836,plain,
! [X4564,X4565] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4565,X4564),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4564,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4565)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4564,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4565))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4565,X4564),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__less__0__iff])]) ).
fof(i_0_1837,plain,
! [X4889,X4890] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4890,X4889),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4889,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4890)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4889,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4890))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4890,X4889),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__le__0__iff])]) ).
cnf(i_0_1838,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1295]) ).
fof(i_0_1839,plain,
! [X4301,X4302,X4303] :
( ( ~ c_Orderings_Oord__class_Oless(X4303,X4302,X4301)
| c_Orderings_Oord__class_Oless(X4303,c_Groups_Ominus__class_Ominus(X4303,X4302,X4301),c_Groups_Ozero__class_Ozero(X4303))
| ~ class_Groups_Oordered__ab__group__add(X4303) )
& ( ~ c_Orderings_Oord__class_Oless(X4303,c_Groups_Ominus__class_Ominus(X4303,X4302,X4301),c_Groups_Ozero__class_Ozero(X4303))
| c_Orderings_Oord__class_Oless(X4303,X4302,X4301)
| ~ class_Groups_Oordered__ab__group__add(X4303) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).
fof(i_0_1840,plain,
! [X3611,X3612,X3613] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3613,X3612,X3611)
| c_Orderings_Oord__class_Oless__eq(X3613,c_Groups_Ominus__class_Ominus(X3613,X3612,X3611),c_Groups_Ozero__class_Ozero(X3613))
| ~ class_Groups_Oordered__ab__group__add(X3613) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3613,c_Groups_Ominus__class_Ominus(X3613,X3612,X3611),c_Groups_Ozero__class_Ozero(X3613))
| c_Orderings_Oord__class_Oless__eq(X3613,X3612,X3611)
| ~ class_Groups_Oordered__ab__group__add(X3613) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).
cnf(i_0_1841,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1296]) ).
cnf(i_0_1842,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
inference(split_conjunct,[status(thm)],[i_0_1297]) ).
cnf(i_0_1843,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
inference(split_conjunct,[status(thm)],[i_0_1298]) ).
fof(i_0_1844,plain,
! [X3445,X3446,X3447,X3448] :
( ~ class_Rings_Ocomm__semiring__0(X3448)
| c_Polynomial_Osmult(X3448,X3447,c_Polynomial_Omonom(X3448,X3446,X3445)) = c_Polynomial_Omonom(X3448,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3448),X3447),X3446),X3445) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__monom])]) ).
fof(i_0_1845,plain,
! [X3441,X3442,X3443,X3444] :
( ~ class_Rings_Ocomm__semiring__0(X3444)
| c_Polynomial_Osmult(X3444,X3443,c_Polynomial_Osmult(X3444,X3442,X3441)) = c_Polynomial_Osmult(X3444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3444),X3443),X3442),X3441) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__smult])]) ).
fof(i_0_1846,plain,
! [X5397,X5398,X5399] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5399,X5398)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5399,X5397)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5399,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5398,X5397)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat])]) ).
fof(i_0_1847,plain,
! [X4322,X4323] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4323)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4323),X4322)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4322)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4323),X4322)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4323)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4322)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4323),X4322)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).
fof(i_0_1848,plain,
! [X4867,X4868] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4868)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4867)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4868),X4867)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])]) ).
fof(i_0_1849,plain,
! [X5203,X5204] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5204)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5203)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5204),X5203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
cnf(i_0_1850,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1299]) ).
cnf(i_0_1851,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1300]) ).
cnf(i_0_1852,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1301]) ).
fof(i_0_1853,plain,
! [X3246] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3246,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3246),X3246))),
inference(variable_rename,[status(thm)],[fact_le__cube]) ).
cnf(i_0_1854,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1302]) ).
cnf(i_0_1855,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1303]) ).
fof(i_0_1856,plain,
! [X4128,X4129,X4130,X4131,X4132] :
( ( ~ c_Orderings_Oord__class_Oless(X4132,X4131,X4130)
| c_Orderings_Oord__class_Oless(X4132,X4129,X4128)
| c_Groups_Ominus__class_Ominus(X4132,X4131,X4130) != c_Groups_Ominus__class_Ominus(X4132,X4129,X4128)
| ~ class_Groups_Oordered__ab__group__add(X4132) )
& ( ~ c_Orderings_Oord__class_Oless(X4132,X4129,X4128)
| c_Orderings_Oord__class_Oless(X4132,X4131,X4130)
| c_Groups_Ominus__class_Ominus(X4132,X4131,X4130) != c_Groups_Ominus__class_Ominus(X4132,X4129,X4128)
| ~ class_Groups_Oordered__ab__group__add(X4132) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).
fof(i_0_1857,plain,
! [X3514,X3515,X3516,X3517,X3518] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3518,X3517,X3516)
| c_Orderings_Oord__class_Oless__eq(X3518,X3515,X3514)
| c_Groups_Ominus__class_Ominus(X3518,X3517,X3516) != c_Groups_Ominus__class_Ominus(X3518,X3515,X3514)
| ~ class_Groups_Oordered__ab__group__add(X3518) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3518,X3515,X3514)
| c_Orderings_Oord__class_Oless__eq(X3518,X3517,X3516)
| c_Groups_Ominus__class_Ominus(X3518,X3517,X3516) != c_Groups_Ominus__class_Ominus(X3518,X3515,X3514)
| ~ class_Groups_Oordered__ab__group__add(X3518) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).
fof(i_0_1858,plain,
! [X5418,X5419] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5418),X5419),X5419)
| X5418 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5419) )
& ( X5418 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5418),X5419),X5419)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5419) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2])])]) ).
fof(i_0_1859,plain,
! [X5416,X5417] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5417),X5416),X5417)
| X5416 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5417) )
& ( X5416 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5417),X5416),X5417)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5417) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1])])]) ).
fof(i_0_1860,plain,
! [X3285,X3286,X3287] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3287,X3286)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3287),X3285),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3286),X3285)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).
fof(i_0_1861,plain,
! [X3288,X3289,X3290] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3290,X3289)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3288),X3290),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3288),X3289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).
fof(i_0_1862,plain,
! [X3379,X3380,X3381,X3382] :
( ~ class_Rings_Ocomm__semiring__1(X3382)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3382),X3381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3382),X3380),X3379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3382),X3380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3382),X3381),X3379)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
fof(i_0_1863,plain,
! [X3727,X3728,X3729] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3729,X3728),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3729,X3727)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3728,X3727),
inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).
fof(i_0_1864,plain,
! [X3730,X3731,X3732] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3732,X3731),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3730,X3731)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3732,X3730),
inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).
fof(i_0_1865,plain,
! [X3741,X3742,X3743] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3743,X3742),X3741) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3743,X3741),X3742),
inference(variable_rename,[status(thm)],[fact_diff__commute]) ).
fof(i_0_1866,plain,
! [X3715,X3716,X3717] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3717,X3716),X3715) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3717,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3716,X3715)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(i_0_1867,plain,
! [X5155,X5156,X5157] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5157,X5156),X5155) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5157,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5156,X5155)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_1868,plain,
! [X3712,X3713,X3714] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3714,X3713),X3712) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3714,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3713,X3712)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_1869,plain,
! [X5152,X5153,X5154] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5154,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5153,X5152)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5153,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5154,X5152)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_1870,plain,
! [X3702,X3703,X3704] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3704,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3703,X3702)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3703,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3704,X3702)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_1871,plain,
! [X5130,X5131] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5131,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5130,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5131,X5130)
| X5131 = X5130 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5131,X5130)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5131,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5130,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( X5131 != X5130
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5131,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5130,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])]) ).
cnf(i_0_1872,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1304]) ).
cnf(i_0_1873,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1305]) ).
cnf(i_0_1874,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1306]) ).
cnf(i_0_1875,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1307]) ).
fof(i_0_1876,plain,
! [X5117,X5118] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5118,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5117)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5118,X5117) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5118,X5117)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5118,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5117) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).
cnf(i_0_1877,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1308]) ).
cnf(i_0_1878,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1309]) ).
cnf(i_0_1879,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1310]) ).
cnf(i_0_1880,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1311]) ).
cnf(i_0_1881,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1312]) ).
fof(i_0_1882,plain,
! [X5115,X5116] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5116,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5115,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5116,X5115) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5116,X5115)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5116,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5115,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq])]) ).
fof(i_0_1883,plain,
! [X5113,X5114] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5114,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5113,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5114,X5113) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5114,X5113)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5114,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5113,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le])]) ).
cnf(i_0_1884,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1313]) ).
fof(i_0_1885,plain,
! [X5270,X5271,X5272,X5273] :
( ~ class_Rings_Ocomm__semiring__1(X5273)
| ~ c_Rings_Odvd__class_Odvd(X5273,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5273),X5272),X5271),X5270)
| c_Rings_Odvd__class_Odvd(X5273,X5272,X5270) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__left])]) ).
fof(i_0_1886,plain,
! [X5274,X5275,X5276,X5277] :
( ~ class_Rings_Ocomm__semiring__1(X5277)
| ~ c_Rings_Odvd__class_Odvd(X5277,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5277),X5276),X5275),X5274)
| c_Rings_Odvd__class_Odvd(X5277,X5275,X5274) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])]) ).
cnf(i_0_1887,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1314]) ).
fof(i_0_1888,plain,
! [X5469,X5470,X5471] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5471,X5469)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5470,X5469)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5469,X5470)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5471,X5470) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5469,X5471)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5470,X5469)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5469,X5470)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5471,X5470) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1315])])]) ).
fof(i_0_1889,plain,
! [X5487,X5488,X5489] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5489,X5487)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5488,X5487)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5489,X5488)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5488,X5489) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5487,X5489)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5488,X5487)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5489,X5488)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5488,X5489) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1316])])]) ).
fof(i_0_1890,plain,
! [X5111,X5112] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5112,X5111)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5112,X5111),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5112,X5111),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5112,X5111) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).
fof(i_0_1891,plain,
! [X3620,X3621] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3621,X3620)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3621,X3620),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3621,X3620),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3621,X3620) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff])]) ).
fof(i_0_1892,plain,
! [X4336,X4337] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4337,X4336))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4336,X4337) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4336,X4337)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4337,X4336)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
cnf(i_0_1893,plain,
( c_Nat_OSuc(X1) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1317]) ).
fof(i_0_1894,plain,
! [X4154,X4155,X4156,X4157] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4157,X4156)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4155,X4156) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4157,X4154)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4155,X4154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_1895,plain,
! [X5590,X5591] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5591)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5591,c_RealDef_Oreal(tc_Nat_Onat,X5590))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X5591),X5590) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__add])]) ).
fof(i_0_1896,plain,
! [X5584,X5585] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5585)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5585,c_RealDef_Oreal(tc_Nat_Onat,X5584))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5585),X5584) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add])]) ).
fof(i_0_1897,plain,
! [X4151,X4152,X4153] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4153,X4152),X4151)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4153,X4151) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_1898,plain,
! [X3349,X3350,X3351] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3351,X3349)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3351,X3350),X3349) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3350,X3349)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3351,X3350),X3349) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1318])])]) ).
fof(i_0_1899,plain,
! [X3346,X3347,X3348] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3348,X3347),X3346)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3348,X3346) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_1900,plain,
! [X3343,X3344,X3345] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3345,X3344),X3343)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3344,X3343) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_1901,plain,
! [X5371,X5372] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5372,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5371,X5372))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5372,X5371) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5372,X5371)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5372,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5371,X5372)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__reduce])]) ).
fof(i_0_1902,plain,
! [X5558,X5559] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5559,X5558)
| c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5558,X5559)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5558),c_RealDef_Oreal(tc_Nat_Onat,X5559)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__diff])]) ).
cnf(i_0_1903,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1319]) ).
cnf(i_0_1904,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))),
inference(split_conjunct,[status(thm)],[i_0_1320]) ).
cnf(i_0_1905,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| 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_1321]) ).
cnf(i_0_1906,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1322]) ).
cnf(i_0_1907,plain,
( X2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk18_2(X2,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1314]) ).
fof(i_0_1908,plain,
! [X3012,X3013,X3014] :
( ( X3013 = c_Groups_Ozero__class_Ozero(X3014)
| c_Groups_Oplus__class_Oplus(X3014,X3013,X3012) != c_Groups_Ozero__class_Ozero(X3014)
| ~ c_Orderings_Oord__class_Oless__eq(X3014,c_Groups_Ozero__class_Ozero(X3014),X3012)
| ~ c_Orderings_Oord__class_Oless__eq(X3014,c_Groups_Ozero__class_Ozero(X3014),X3013)
| ~ class_Groups_Oordered__comm__monoid__add(X3014) )
& ( X3012 = c_Groups_Ozero__class_Ozero(X3014)
| c_Groups_Oplus__class_Oplus(X3014,X3013,X3012) != c_Groups_Ozero__class_Ozero(X3014)
| ~ c_Orderings_Oord__class_Oless__eq(X3014,c_Groups_Ozero__class_Ozero(X3014),X3012)
| ~ c_Orderings_Oord__class_Oless__eq(X3014,c_Groups_Ozero__class_Ozero(X3014),X3013)
| ~ class_Groups_Oordered__comm__monoid__add(X3014) )
& ( X3013 != c_Groups_Ozero__class_Ozero(X3014)
| X3012 != c_Groups_Ozero__class_Ozero(X3014)
| c_Groups_Oplus__class_Oplus(X3014,X3013,X3012) = c_Groups_Ozero__class_Ozero(X3014)
| ~ c_Orderings_Oord__class_Oless__eq(X3014,c_Groups_Ozero__class_Ozero(X3014),X3012)
| ~ c_Orderings_Oord__class_Oless__eq(X3014,c_Groups_Ozero__class_Ozero(X3014),X3013)
| ~ class_Groups_Oordered__comm__monoid__add(X3014) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_1909,plain,
! [X4642,X4643,X4644,X4645] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4644,X4645),X4643,X4642)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4644,X4645),X4643,X4642)
| ~ class_Orderings_Oord(X4645) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4644,X4645),X4642,X4643)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4644,X4645),X4643,X4642)
| ~ class_Orderings_Oord(X4645) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4644,X4645),X4643,X4642)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4644,X4645),X4642,X4643)
| c_Orderings_Oord__class_Oless(tc_fun(X4644,X4645),X4643,X4642)
| ~ class_Orderings_Oord(X4645) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1323])])]) ).
fof(i_0_1910,plain,
! [X5657,X5658,X5659] :
( ~ class_Divides_Oring__div(X5659)
| ~ c_Rings_Odvd__class_Odvd(X5659,X5658,X5657)
| c_Divides_Odiv__class_Odiv(X5659,c_Groups_Ouminus__class_Ouminus(X5659,X5657),X5658) = c_Groups_Ouminus__class_Ouminus(X5659,c_Divides_Odiv__class_Odiv(X5659,X5657,X5658)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__neg__div])]) ).
fof(i_0_1911,plain,
! [X5660,X5661,X5662] :
( ~ class_Divides_Oring__div(X5662)
| ~ c_Rings_Odvd__class_Odvd(X5662,X5661,X5660)
| c_Divides_Odiv__class_Odiv(X5662,X5660,c_Groups_Ouminus__class_Ouminus(X5662,X5661)) = c_Groups_Ouminus__class_Ouminus(X5662,c_Divides_Odiv__class_Odiv(X5662,X5660,X5661)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__neg])]) ).
cnf(i_0_1912,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1324]) ).
fof(i_0_1913,plain,
! [X5107,X5108] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5108),X5107))
| X5107 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5108) )
& ( X5107 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5108),X5107)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5108)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5108),X5107)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])]) ).
fof(i_0_1914,plain,
! [X4992,X4993] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4993),X4992))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4993)
| X4992 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4993)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4993),X4992)) )
& ( X4992 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4993),X4992)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
fof(i_0_1915,plain,
! [X4503,X4504,X4505] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X4505),X4504,X4503)
| c_Polynomial_Opos__poly(X4505,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4505),X4503,X4504))
| ~ class_Rings_Olinordered__idom(X4505) )
& ( ~ c_Polynomial_Opos__poly(X4505,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4505),X4503,X4504))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X4505),X4504,X4503)
| ~ class_Rings_Olinordered__idom(X4505) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__poly__def])])]) ).
fof(i_0_1916,plain,
! [X4884,X4885,X4886] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X4886),X4885,X4884)
| X4885 = X4884
| c_Polynomial_Opos__poly(X4886,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4886),X4884,X4885))
| ~ class_Rings_Olinordered__idom(X4886) )
& ( X4885 != X4884
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X4886),X4885,X4884)
| ~ class_Rings_Olinordered__idom(X4886) )
& ( ~ c_Polynomial_Opos__poly(X4886,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4886),X4884,X4885))
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X4886),X4885,X4884)
| ~ class_Rings_Olinordered__idom(X4886) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__poly__def])])]) ).
fof(i_0_1917,plain,
! [X3161,X3162,X3163] :
( ~ class_Rings_Ocomm__semiring__0(X3163)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3163,c_Polynomial_OpCons(X3163,X3162,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3163))),X3161) = c_Polynomial_OpCons(X3163,X3162,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3163))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__single])]) ).
fof(i_0_1918,plain,
! [X5304,X5305,X5306,X5307] :
( ~ class_Fields_Ofield(X5307)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5307),X5306,X5305)
| X5304 = c_Groups_Ozero__class_Ozero(X5307)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5307),c_Polynomial_Osmult(X5307,X5304,X5306),X5305) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd])]) ).
fof(i_0_1919,plain,
! [X4485,X4486,X4487] :
( ( X4485 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4487))
| c_Polynomial_Opos__poly(X4487,X4485)
| ~ c_Polynomial_Opos__poly(X4487,c_Polynomial_OpCons(X4487,X4486,X4485))
| ~ class_Rings_Olinordered__idom(X4487) )
& ( c_Orderings_Oord__class_Oless(X4487,c_Groups_Ozero__class_Ozero(X4487),X4486)
| c_Polynomial_Opos__poly(X4487,X4485)
| ~ c_Polynomial_Opos__poly(X4487,c_Polynomial_OpCons(X4487,X4486,X4485))
| ~ class_Rings_Olinordered__idom(X4487) )
& ( ~ c_Polynomial_Opos__poly(X4487,X4485)
| c_Polynomial_Opos__poly(X4487,c_Polynomial_OpCons(X4487,X4486,X4485))
| ~ class_Rings_Olinordered__idom(X4487) )
& ( X4485 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4487))
| ~ c_Orderings_Oord__class_Oless(X4487,c_Groups_Ozero__class_Ozero(X4487),X4486)
| c_Polynomial_Opos__poly(X4487,c_Polynomial_OpCons(X4487,X4486,X4485))
| ~ class_Rings_Olinordered__idom(X4487) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__pCons])])]) ).
fof(i_0_1920,plain,
! [X5288,X5289,X5290,X5291] :
( ~ class_Rings_Ocomm__semiring__1(X5291)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5291),X5290,X5289)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5291),X5290,c_Polynomial_Osmult(X5291,X5288,X5289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__smult])]) ).
cnf(i_0_1921,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1325]) ).
fof(i_0_1922,plain,
! [X5019,X5020,X5021,X5022] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X5022),X5021),X5020) != hAPP(hAPP(c_Power_Opower__class_Opower(X5022),X5021),X5019)
| X5020 = X5019
| ~ c_Orderings_Oord__class_Oless(X5022,c_Groups_Oone__class_Oone(X5022),X5021)
| ~ class_Rings_Olinordered__semidom(X5022) )
& ( X5020 != X5019
| hAPP(hAPP(c_Power_Opower__class_Opower(X5022),X5021),X5020) = hAPP(hAPP(c_Power_Opower__class_Opower(X5022),X5021),X5019)
| ~ c_Orderings_Oord__class_Oless(X5022,c_Groups_Oone__class_Oone(X5022),X5021)
| ~ class_Rings_Olinordered__semidom(X5022) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_1923,plain,
! [X5580,X5581] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5581)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5581,c_RealDef_Oreal(tc_Nat_Onat,X5580))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X5581),X5580) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__natfloor])]) ).
fof(i_0_1924,plain,
! [X5570,X5571] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5571),X5570)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5571,c_RealDef_Oreal(tc_Nat_Onat,X5570))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5571) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5571,c_RealDef_Oreal(tc_Nat_Onat,X5570))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5571),X5570)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5571) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq])])]) ).
fof(i_0_1925,plain,
! [X5568,X5569] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5568,c_RComplete_Onatfloor(X5569))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5568),X5569)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5569) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5568),X5569)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5568,c_RComplete_Onatfloor(X5569))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5569) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq])])]) ).
cnf(i_0_1926,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1326]) ).
fof(i_0_1927,plain,
! [X5010,X5011,X5012] :
( ~ class_Rings_Olinordered__semidom(X5012)
| ~ c_Orderings_Oord__class_Oless(X5012,c_Groups_Ozero__class_Ozero(X5012),X5011)
| c_Orderings_Oord__class_Oless(X5012,c_Groups_Ozero__class_Ozero(X5012),hAPP(hAPP(c_Power_Opower__class_Opower(X5012),X5011),X5010)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_1928,plain,
! [X5013,X5014,X5015] :
( ~ class_Rings_Olinordered__semidom(X5015)
| ~ c_Orderings_Oord__class_Oless__eq(X5015,c_Groups_Oone__class_Oone(X5015),X5014)
| c_Orderings_Oord__class_Oless__eq(X5015,c_Groups_Oone__class_Oone(X5015),hAPP(hAPP(c_Power_Opower__class_Opower(X5015),X5014),X5013)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).
fof(i_0_1929,plain,
! [X5003,X5004,X5005] :
( ~ class_Rings_Olinordered__semidom(X5005)
| ~ c_Orderings_Oord__class_Oless__eq(X5005,c_Groups_Ozero__class_Ozero(X5005),X5004)
| c_Orderings_Oord__class_Oless__eq(X5005,c_Groups_Ozero__class_Ozero(X5005),hAPP(hAPP(c_Power_Opower__class_Opower(X5005),X5004),X5003)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).
fof(i_0_1930,plain,
! [X5207] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5207)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5207,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X5207),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__add__one])]) ).
fof(i_0_1931,plain,
! [X4856] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4856)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4856,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X4856),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add__one])]) ).
cnf(i_0_1932,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1295]) ).
fof(i_0_1933,plain,
! [X4216,X4217] :
( ~ class_Rings_Olinordered__ring(X4217)
| ~ c_Orderings_Oord__class_Oless(X4217,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4217),X4216),X4216),c_Groups_Ozero__class_Ozero(X4217)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1327])]) ).
fof(i_0_1934,plain,
! [X5158] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5158),X5158) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
fof(i_0_1935,plain,
! [X5578,X5579] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5579)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5578)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X5579,X5578)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).
fof(i_0_1936,plain,
! [X5212,X5213,X5214,X5215] : hAPP(hAPP(c_Power_Opower_Opower(X5215,X5214,X5213),X5212),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5214,
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(i_0_1937,plain,
! [X5404,X5405] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5405)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5405,X5404)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5404,X5405) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1328])]) ).
fof(i_0_1938,plain,
! [X5377,X5378] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5378)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5378,X5377)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5377,X5378) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1329])]) ).
cnf(i_0_1939,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_1330]) ).
cnf(i_0_1940,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = 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_1331]) ).
cnf(i_0_1941,plain,
( X1 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(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_1332]) ).
fof(i_0_1942,plain,
! [X5119] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5119)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).
fof(i_0_1943,plain,
! [X5689,X5690,X5691] :
( ~ class_Divides_Osemiring__div(X5691)
| ~ c_Rings_Odvd__class_Odvd(X5691,X5690,X5689)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5691),X5690),c_Divides_Odiv__class_Odiv(X5691,X5689,X5690)) = X5689 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel])]) ).
cnf(i_0_1944,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1284]) ).
fof(i_0_1945,plain,
! [X5335,X5336,X5337] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5336)
| c_Rings_Odvd__class_Odvd(X5337,X5335,hAPP(hAPP(c_Power_Opower__class_Opower(X5337),X5335),X5336))
| ~ class_Rings_Ocomm__semiring__1(X5337) )
& ( X5335 != c_Groups_Oone__class_Oone(X5337)
| c_Rings_Odvd__class_Odvd(X5337,X5335,hAPP(hAPP(c_Power_Opower__class_Opower(X5337),X5335),X5336))
| ~ class_Rings_Ocomm__semiring__1(X5337) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power])])]) ).
fof(i_0_1946,plain,
! [X4518,X4519,X4520] :
( ~ class_Groups_Oab__group__add(X4520)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4520),c_Polynomial_OpCons(X4520,X4519,X4518)) = c_Polynomial_OpCons(X4520,c_Groups_Ouminus__class_Ouminus(X4520,X4519),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4520),X4518)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I2_J])]) ).
fof(i_0_1947,plain,
! [X4515,X4516,X4517] :
( ~ class_Groups_Oab__group__add(X4517)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4517),c_Polynomial_OpCons(X4517,X4516,X4515)) = c_Polynomial_OpCons(X4517,c_Groups_Ouminus__class_Ouminus(X4517,X4516),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4517),X4515)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__pCons])]) ).
cnf(i_0_1948,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1289]) ).
fof(i_0_1949,plain,
! [X5253,X5254,X5255,X5256] :
( ~ class_Rings_Ocomm__semiring__1(X5256)
| ~ c_Rings_Odvd__class_Odvd(X5256,X5255,X5254)
| c_Rings_Odvd__class_Odvd(X5256,X5255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5254),X5253)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult2])]) ).
fof(i_0_1950,plain,
! [X5257,X5258,X5259,X5260] :
( ~ class_Rings_Ocomm__semiring__1(X5260)
| ~ c_Rings_Odvd__class_Odvd(X5260,X5259,X5258)
| c_Rings_Odvd__class_Odvd(X5260,X5259,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5260),X5257),X5258)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult])]) ).
fof(i_0_1951,plain,
! [X3537,X3538,X3539] :
( ~ class_RealVector_Oreal__normed__vector(X3539)
| c_RealVector_Onorm__class_Onorm(X3539,c_Groups_Ominus__class_Ominus(X3539,X3538,X3537)) = c_RealVector_Onorm__class_Onorm(X3539,c_Groups_Ominus__class_Ominus(X3539,X3537,X3538)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__commute])]) ).
fof(i_0_1952,plain,
! [X3458,X3459,X3460] :
( ~ class_RealVector_Oreal__normed__div__algebra(X3460)
| c_RealVector_Onorm__class_Onorm(X3460,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3460),X3459),X3458)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3460,X3459)),c_RealVector_Onorm__class_Onorm(X3460,X3458)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])]) ).
fof(i_0_1953,plain,
! [X5120,X5121] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5121,X5120)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5121,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5120) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).
cnf(i_0_1954,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1333]) ).
cnf(i_0_1955,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1310]) ).
cnf(i_0_1956,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1311]) ).
cnf(i_0_1957,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1334]) ).
cnf(i_0_1958,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1307]) ).
cnf(i_0_1959,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1335]) ).
cnf(i_0_1960,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1313]) ).
cnf(i_0_1961,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1284]) ).
cnf(i_0_1962,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1336]) ).
fof(i_0_1963,plain,
! [X4176,X4177] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4177,X4176),X4177),
inference(variable_rename,[status(thm)],[i_0_1337]) ).
fof(i_0_1964,plain,
! [X4174,X4175] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4175,X4174),X4174),
inference(variable_rename,[status(thm)],[i_0_1338]) ).
fof(i_0_1965,plain,
! [X3307,X3308] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3308,X3307)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3307,X3308),X3308) = X3307 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).
fof(i_0_1966,plain,
! [X3297,X3298] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3298,X3297)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3297,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3297,X3298)) = X3298 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).
fof(i_0_1967,plain,
! [X3299,X3300] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3300,X3299)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3300,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3299,X3300)) = X3299 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
fof(i_0_1968,plain,
! [X3063,X3064,X3065,X3066,X3067] :
( ~ class_Orderings_Oord(X3067)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3066,X3067),X3065,X3064)
| c_Orderings_Oord__class_Oless__eq(X3067,hAPP(X3065,X3063),hAPP(X3064,X3063)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_1969,plain,
! [X3025,X3026,X3027,X3028,X3029] :
( ~ class_Orderings_Oord(X3029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3028,X3029),X3027,X3026)
| c_Orderings_Oord__class_Oless__eq(X3029,hAPP(X3027,X3025),hAPP(X3026,X3025)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_1970,plain,
! [X4199,X4200,X4201] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4201,X4200)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4201,X4199),X4200) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).
fof(i_0_1971,plain,
! [X4181,X4182,X4183] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4183,X4182)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4183,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4182,X4181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_1972,plain,
! [X4168,X4169,X4170] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4170,X4169)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4170,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4169,X4168)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_1973,plain,
! [X4178,X4179,X4180] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4180,X4179)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4180,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4178,X4179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_1974,plain,
! [X4165,X4166,X4167] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4167,X4166)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4167,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4165,X4166)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_1975,plain,
! [X3884,X3885,X3886] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3886,X3885)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3886,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3885,X3884)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_1976,plain,
! [X3273,X3274,X3275] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3275,X3274)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3275,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3274,X3273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_1977,plain,
! [X3887,X3888,X3889] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3889,X3888)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3889,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3887,X3888)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_1978,plain,
! [X3276,X3277,X3278] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3278,X3277)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3278,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3276,X3277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
cnf(i_0_1979,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| 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_1321]) ).
cnf(i_0_1980,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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_1321]) ).
cnf(i_0_1981,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1322]) ).
cnf(i_0_1982,plain,
( X1 = 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) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1322]) ).
fof(i_0_1983,plain,
! [X5648,X5649,X5650,X5651] :
( ( c_Divides_Odiv__class_Odiv(X5651,X5649,X5650) != X5648
| X5649 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5651),X5648),X5650)
| ~ c_Rings_Odvd__class_Odvd(X5651,X5650,X5649)
| X5650 = c_Groups_Ozero__class_Ozero(X5651)
| ~ class_Divides_Osemiring__div(X5651) )
& ( X5649 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5651),X5648),X5650)
| c_Divides_Odiv__class_Odiv(X5651,X5649,X5650) = X5648
| ~ c_Rings_Odvd__class_Odvd(X5651,X5650,X5649)
| X5650 = c_Groups_Ozero__class_Ozero(X5651)
| ~ class_Divides_Osemiring__div(X5651) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__eq__mult])])]) ).
fof(i_0_1984,plain,
! [X5109] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5109),X5109))
| X5109 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X5109 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5109),X5109)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1339])]) ).
fof(i_0_1985,plain,
! [X4316,X4317,X4318] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4318),X4317) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4318),X4316)
| X4317 = X4316
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4318) )
& ( X4317 != X4316
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4318),X4317) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4318),X4316)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4318) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
fof(i_0_1986,plain,
! [X5201,X5202] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5202)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5202),X5201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).
fof(i_0_1987,plain,
! [X5687,X5688] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5688,X5687)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5688),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5687,X5688)) = X5687 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mult__div__cancel])]) ).
fof(i_0_1988,plain,
! [X5280,X5281,X5282,X5283] :
( ~ class_Rings_Ocomm__semiring__1(X5283)
| ~ c_Rings_Odvd__class_Odvd(X5283,X5282,X5281)
| ~ c_Rings_Odvd__class_Odvd(X5283,X5281,X5280)
| c_Rings_Odvd__class_Odvd(X5283,X5282,X5280) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__trans])]) ).
fof(i_0_1989,plain,
! [X3954,X3955,X3956,X3957] :
( ~ class_Orderings_Opreorder(X3957)
| ~ c_Orderings_Oord__class_Oless(X3957,X3956,X3955)
| ~ c_Orderings_Oord__class_Oless(X3957,X3955,X3954)
| c_Orderings_Oord__class_Oless(X3957,X3956,X3954) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_1990,plain,
! [X4034,X4035,X4036,X4037] :
( ~ class_Orderings_Opreorder(X4037)
| ~ c_Orderings_Oord__class_Oless__eq(X4037,X4036,X4035)
| ~ c_Orderings_Oord__class_Oless(X4037,X4035,X4034)
| c_Orderings_Oord__class_Oless(X4037,X4036,X4034) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_1991,plain,
! [X4042,X4043,X4044,X4045] :
( ~ class_Orderings_Opreorder(X4045)
| ~ c_Orderings_Oord__class_Oless(X4045,X4044,X4043)
| ~ c_Orderings_Oord__class_Oless__eq(X4045,X4043,X4042)
| c_Orderings_Oord__class_Oless(X4045,X4044,X4042) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_1992,plain,
! [X3950,X3951,X3952,X3953] :
( ~ class_Orderings_Oorder(X3953)
| ~ c_Orderings_Oord__class_Oless(X3953,X3952,X3951)
| ~ c_Orderings_Oord__class_Oless(X3953,X3950,X3952)
| c_Orderings_Oord__class_Oless(X3953,X3950,X3951) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_1993,plain,
! [X4030,X4031,X4032,X4033] :
( ~ class_Orderings_Oorder(X4033)
| ~ c_Orderings_Oord__class_Oless__eq(X4033,X4032,X4031)
| ~ c_Orderings_Oord__class_Oless(X4033,X4030,X4032)
| c_Orderings_Oord__class_Oless(X4033,X4030,X4031) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_1994,plain,
! [X4038,X4039,X4040,X4041] :
( ~ class_Orderings_Oorder(X4041)
| ~ c_Orderings_Oord__class_Oless(X4041,X4040,X4039)
| ~ c_Orderings_Oord__class_Oless__eq(X4041,X4038,X4040)
| c_Orderings_Oord__class_Oless(X4041,X4038,X4039) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_1995,plain,
! [X3037,X3038,X3039,X3040] :
( ~ class_Orderings_Opreorder(X3040)
| ~ c_Orderings_Oord__class_Oless__eq(X3040,X3039,X3038)
| ~ c_Orderings_Oord__class_Oless__eq(X3040,X3038,X3037)
| c_Orderings_Oord__class_Oless__eq(X3040,X3039,X3037) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_1996,plain,
! [X3030,X3031,X3032,X3033] :
( ~ class_Orderings_Oorder(X3033)
| ~ c_Orderings_Oord__class_Oless__eq(X3033,X3032,X3031)
| ~ c_Orderings_Oord__class_Oless__eq(X3033,X3030,X3032)
| c_Orderings_Oord__class_Oless__eq(X3033,X3030,X3031) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_1997,plain,
! [X5629,X5630,X5631] :
( ~ class_Groups_Oab__group__add(X5631)
| c_Groups_Ominus__class_Ominus(X5631,c_Groups_Ouminus__class_Ouminus(X5631,X5630),c_Groups_Ouminus__class_Ouminus(X5631,X5629)) = c_Groups_Ouminus__class_Ouminus(X5631,c_Groups_Ominus__class_Ominus(X5631,X5630,X5629)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus])]) ).
fof(i_0_1998,plain,
! [X4627,X4628,X4629] :
( ~ class_Groups_Oab__group__add(X4629)
| c_Groups_Ouminus__class_Ouminus(X4629,c_Groups_Oplus__class_Oplus(X4629,X4628,X4627)) = c_Groups_Oplus__class_Oplus(X4629,c_Groups_Ouminus__class_Ouminus(X4629,X4628),c_Groups_Ouminus__class_Ouminus(X4629,X4627)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).
fof(i_0_1999,plain,
! [X4630,X4631,X4632] :
( ~ class_Groups_Ogroup__add(X4632)
| c_Groups_Ouminus__class_Ouminus(X4632,c_Groups_Oplus__class_Oplus(X4632,X4631,X4630)) = c_Groups_Oplus__class_Oplus(X4632,c_Groups_Ouminus__class_Ouminus(X4632,X4630),c_Groups_Ouminus__class_Ouminus(X4632,X4631)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).
fof(i_0_2000,plain,
! [X5572] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5572,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5572)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__add__one__gt]) ).
fof(i_0_2001,plain,
! [X4593,X4594,X4595] :
( ( ~ c_Orderings_Oord__class_Oless(X4595,c_Groups_Ouminus__class_Ouminus(X4595,X4594),c_Groups_Ouminus__class_Ouminus(X4595,X4593))
| c_Orderings_Oord__class_Oless(X4595,X4593,X4594)
| ~ class_Groups_Oordered__ab__group__add(X4595) )
& ( ~ c_Orderings_Oord__class_Oless(X4595,X4593,X4594)
| c_Orderings_Oord__class_Oless(X4595,c_Groups_Ouminus__class_Ouminus(X4595,X4594),c_Groups_Ouminus__class_Ouminus(X4595,X4593))
| ~ class_Groups_Oordered__ab__group__add(X4595) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).
fof(i_0_2002,plain,
! [X4581,X4582,X4583] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4583,c_Groups_Ouminus__class_Ouminus(X4583,X4582),c_Groups_Ouminus__class_Ouminus(X4583,X4581))
| c_Orderings_Oord__class_Oless__eq(X4583,X4581,X4582)
| ~ class_Groups_Oordered__ab__group__add(X4583) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4583,X4581,X4582)
| c_Orderings_Oord__class_Oless__eq(X4583,c_Groups_Ouminus__class_Ouminus(X4583,X4582),c_Groups_Ouminus__class_Ouminus(X4583,X4581))
| ~ class_Groups_Oordered__ab__group__add(X4583) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).
cnf(i_0_2003,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1340]) ).
fof(i_0_2004,plain,
! [X5499,X5500] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5500)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5499,X5500)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5499) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__pos__nat])]) ).
fof(i_0_2005,plain,
! [X5709,X5710] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5710)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5710,X5709)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5710,X5709) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial])]) ).
fof(i_0_2006,plain,
! [X5696,X5697] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5697,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5697)
| X5696 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5697,X5696) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5696,X5697)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5697)
| X5696 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5697,X5696) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5697,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5697,X5696)
| X5696 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5697,X5696) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5696,X5697)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5697,X5696)
| X5696 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5697,X5696) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X5696 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5697,X5696) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5697)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5697,X5696)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5697,X5696) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5697,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5696,X5697)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5697,X5696) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff])])]) ).
fof(i_0_2007,plain,
! [X5718,X5719] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5719,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5718,X5719)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5719,X5718) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial])]) ).
fof(i_0_2008,plain,
! [X4620,X4621,X4622] :
( ~ class_RealVector_Oreal__normed__algebra(X4622)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4622),c_Groups_Ouminus__class_Ouminus(X4622,X4621)),X4620) = c_Groups_Ouminus__class_Ouminus(X4622,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4622),X4621),X4620)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus])]) ).
fof(i_0_2009,plain,
! [X4617,X4618,X4619] :
( ~ class_RealVector_Oreal__normed__algebra(X4619)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4619),c_Groups_Ouminus__class_Ouminus(X4619,X4618)),X4617) = c_Groups_Ouminus__class_Ouminus(X4619,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4619),X4618),X4617)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left])]) ).
fof(i_0_2010,plain,
! [X4599,X4600,X4601] :
( ~ class_Rings_Oring(X4601)
| c_Groups_Ouminus__class_Ouminus(X4601,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4601),X4600),X4599)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4601),c_Groups_Ouminus__class_Ouminus(X4601,X4600)),X4599) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).
fof(i_0_2011,plain,
! [X4722,X4723,X4724] :
( ~ class_Rings_Ocomm__ring(X4724)
| c_Polynomial_Osmult(X4724,X4723,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4724),X4722)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4724),c_Polynomial_Osmult(X4724,X4723,X4722)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__minus__right])]) ).
fof(i_0_2012,plain,
! [X5406,X5407] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5407,X5406)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5406)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5407,X5406) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__imp__le])]) ).
fof(i_0_2013,plain,
! [X5408,X5409] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5409,X5408)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5408)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5409,X5408) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__le])]) ).
cnf(i_0_2014,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1324]) ).
cnf(i_0_2015,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1324]) ).
fof(i_0_2016,plain,
! [X3309,X3310,X3311] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3310,X3311) != X3309
| X3310 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3309,X3311)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3311,X3310) )
& ( X3310 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3309,X3311)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3310,X3311) = X3309
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3311,X3310) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).
fof(i_0_2017,plain,
! [X4532,X4533,X4534] :
( ~ class_RealVector_Oreal__normed__div__algebra(X4534)
| c_RealVector_Onorm__class_Onorm(X4534,hAPP(hAPP(c_Power_Opower__class_Opower(X4534),X4533),X4532)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4534,X4533)),X4532) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power])]) ).
fof(i_0_2018,plain,
! [X4633,X4634,X4635] :
( ~ class_Groups_Ogroup__add(X4635)
| c_Groups_Oplus__class_Oplus(X4635,X4634,c_Groups_Oplus__class_Oplus(X4635,c_Groups_Ouminus__class_Ouminus(X4635,X4634),X4633)) = X4633 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).
fof(i_0_2019,plain,
! [X5463,X5464,X5465] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5465,X5464)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5464,X5463)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5465,X5463) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans])]) ).
fof(i_0_2020,plain,
! [X5168,X5169,X5170] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5170,X5169)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5169,X5168)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5170,X5168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).
fof(i_0_2021,plain,
! [X3321,X3322,X3323] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3323,X3322)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3322,X3321)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3323,X3321) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_2022,plain,
! [X3111,X3112,X3113] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3113,X3112)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3112,X3111)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3113,X3111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
cnf(i_0_2023,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1306]) ).
fof(i_0_2024,plain,
! [X4878,X4879,X4880] :
( ~ class_Rings_Olinordered__idom(X4880)
| ~ c_Polynomial_Opos__poly(X4880,X4879)
| ~ c_Polynomial_Opos__poly(X4880,X4878)
| c_Polynomial_Opos__poly(X4880,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4880)),X4879),X4878)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__mult])]) ).
fof(i_0_2025,plain,
! [X5549,X5550] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5550),X5549)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5550)),c_RealDef_Oreal(tc_Nat_Onat,X5549)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__mult]) ).
cnf(i_0_2026,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1290]) ).
cnf(i_0_2027,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1291]) ).
fof(i_0_2028,plain,
! [X4547,X4548,X4549] :
( ~ class_Rings_Ocomm__ring(X4549)
| hAPP(c_Polynomial_Opoly(X4549,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4549),X4548)),X4547) = c_Groups_Ouminus__class_Ouminus(X4549,hAPP(c_Polynomial_Opoly(X4549,X4548),X4547)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__minus])]) ).
fof(i_0_2029,plain,
! [X4590,X4591,X4592] :
( ( ~ c_Orderings_Oord__class_Oless(X4592,c_Groups_Ouminus__class_Ouminus(X4592,X4591),X4590)
| c_Orderings_Oord__class_Oless(X4592,c_Groups_Ouminus__class_Ouminus(X4592,X4590),X4591)
| ~ class_Groups_Oordered__ab__group__add(X4592) )
& ( ~ c_Orderings_Oord__class_Oless(X4592,c_Groups_Ouminus__class_Ouminus(X4592,X4590),X4591)
| c_Orderings_Oord__class_Oless(X4592,c_Groups_Ouminus__class_Ouminus(X4592,X4591),X4590)
| ~ class_Groups_Oordered__ab__group__add(X4592) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).
fof(i_0_2030,plain,
! [X4578,X4579,X4580] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4580,c_Groups_Ouminus__class_Ouminus(X4580,X4579),X4578)
| c_Orderings_Oord__class_Oless__eq(X4580,c_Groups_Ouminus__class_Ouminus(X4580,X4578),X4579)
| ~ class_Groups_Oordered__ab__group__add(X4580) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4580,c_Groups_Ouminus__class_Ouminus(X4580,X4578),X4579)
| c_Orderings_Oord__class_Oless__eq(X4580,c_Groups_Ouminus__class_Ouminus(X4580,X4579),X4578)
| ~ class_Groups_Oordered__ab__group__add(X4580) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).
fof(i_0_2031,plain,
! [X4587,X4588,X4589] :
( ( ~ c_Orderings_Oord__class_Oless(X4589,X4588,c_Groups_Ouminus__class_Ouminus(X4589,X4587))
| c_Orderings_Oord__class_Oless(X4589,X4587,c_Groups_Ouminus__class_Ouminus(X4589,X4588))
| ~ class_Groups_Oordered__ab__group__add(X4589) )
& ( ~ c_Orderings_Oord__class_Oless(X4589,X4587,c_Groups_Ouminus__class_Ouminus(X4589,X4588))
| c_Orderings_Oord__class_Oless(X4589,X4588,c_Groups_Ouminus__class_Ouminus(X4589,X4587))
| ~ class_Groups_Oordered__ab__group__add(X4589) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).
fof(i_0_2032,plain,
! [X4575,X4576,X4577] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4577,X4576,c_Groups_Ouminus__class_Ouminus(X4577,X4575))
| c_Orderings_Oord__class_Oless__eq(X4577,X4575,c_Groups_Ouminus__class_Ouminus(X4577,X4576))
| ~ class_Groups_Oordered__ab__group__add(X4577) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4577,X4575,c_Groups_Ouminus__class_Ouminus(X4577,X4576))
| c_Orderings_Oord__class_Oless__eq(X4577,X4576,c_Groups_Ouminus__class_Ouminus(X4577,X4575))
| ~ class_Groups_Oordered__ab__group__add(X4577) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).
fof(i_0_2033,plain,
! [X5540,X5541] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5541,X5540)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5541),c_RealDef_Oreal(tc_Nat_Onat,X5540)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__add]) ).
fof(i_0_2034,plain,
! [X5138,X5139] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5139,X5138)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5139),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5138)),
inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(i_0_2035,plain,
! [X4540,X4541,X4542] :
( ~ class_Groups_Oab__group__add(X4542)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4542),c_Polynomial_Omonom(X4542,X4541,X4540)) = c_Polynomial_Omonom(X4542,c_Groups_Ouminus__class_Ouminus(X4542,X4541),X4540) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__monom])]) ).
fof(i_0_2036,plain,
! [X4512,X4513,X4514] :
( ~ class_Rings_Ocomm__ring(X4514)
| c_Polynomial_Osmult(X4514,c_Groups_Ouminus__class_Ouminus(X4514,X4513),X4512) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4514),c_Polynomial_Osmult(X4514,X4513,X4512)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__minus__left])]) ).
cnf(i_0_2037,plain,
( 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 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1321]) ).
cnf(i_0_2038,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X1 != 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_1321]) ).
cnf(i_0_2039,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1322]) ).
cnf(i_0_2040,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != 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_1322]) ).
fof(i_0_2041,plain,
! [X4340,X4341] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4341,X4340)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4340,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4341,X4340)) = X4341 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1341])]) ).
fof(i_0_2042,plain,
! [X5538,X5539] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5539),c_RealDef_Oreal(tc_Nat_Onat,X5538))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5539,X5538) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5539,X5538)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5539),c_RealDef_Oreal(tc_Nat_Onat,X5538)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff])]) ).
fof(i_0_2043,plain,
! [X5545,X5546] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5546),c_RealDef_Oreal(tc_Nat_Onat,X5545))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5546,X5545) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5546,X5545)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5546),c_RealDef_Oreal(tc_Nat_Onat,X5545)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff])]) ).
fof(i_0_2044,plain,
! [X4747,X4748] :
( ( ~ c_Orderings_Oord__class_Oless(X4748,c_Groups_Ouminus__class_Ouminus(X4748,X4747),c_Groups_Ozero__class_Ozero(X4748))
| c_Orderings_Oord__class_Oless(X4748,c_Groups_Ozero__class_Ozero(X4748),X4747)
| ~ class_Groups_Oordered__ab__group__add(X4748) )
& ( ~ c_Orderings_Oord__class_Oless(X4748,c_Groups_Ozero__class_Ozero(X4748),X4747)
| c_Orderings_Oord__class_Oless(X4748,c_Groups_Ouminus__class_Ouminus(X4748,X4747),c_Groups_Ozero__class_Ozero(X4748))
| ~ class_Groups_Oordered__ab__group__add(X4748) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).
fof(i_0_2045,plain,
! [X4739,X4740] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4740,c_Groups_Ouminus__class_Ouminus(X4740,X4739),c_Groups_Ozero__class_Ozero(X4740))
| c_Orderings_Oord__class_Oless__eq(X4740,c_Groups_Ozero__class_Ozero(X4740),X4739)
| ~ class_Groups_Oordered__ab__group__add(X4740) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4740,c_Groups_Ozero__class_Ozero(X4740),X4739)
| c_Orderings_Oord__class_Oless__eq(X4740,c_Groups_Ouminus__class_Ouminus(X4740,X4739),c_Groups_Ozero__class_Ozero(X4740))
| ~ class_Groups_Oordered__ab__group__add(X4740) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).
fof(i_0_2046,plain,
! [X4745,X4746] :
( ( ~ c_Orderings_Oord__class_Oless(X4746,c_Groups_Ozero__class_Ozero(X4746),c_Groups_Ouminus__class_Ouminus(X4746,X4745))
| c_Orderings_Oord__class_Oless(X4746,X4745,c_Groups_Ozero__class_Ozero(X4746))
| ~ class_Groups_Oordered__ab__group__add(X4746) )
& ( ~ c_Orderings_Oord__class_Oless(X4746,X4745,c_Groups_Ozero__class_Ozero(X4746))
| c_Orderings_Oord__class_Oless(X4746,c_Groups_Ozero__class_Ozero(X4746),c_Groups_Ouminus__class_Ouminus(X4746,X4745))
| ~ class_Groups_Oordered__ab__group__add(X4746) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).
fof(i_0_2047,plain,
! [X4743,X4744] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4744,c_Groups_Ozero__class_Ozero(X4744),c_Groups_Ouminus__class_Ouminus(X4744,X4743))
| c_Orderings_Oord__class_Oless__eq(X4744,X4743,c_Groups_Ozero__class_Ozero(X4744))
| ~ class_Groups_Oordered__ab__group__add(X4744) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4744,X4743,c_Groups_Ozero__class_Ozero(X4744))
| c_Orderings_Oord__class_Oless__eq(X4744,c_Groups_Ozero__class_Ozero(X4744),c_Groups_Ouminus__class_Ouminus(X4744,X4743))
| ~ class_Groups_Oordered__ab__group__add(X4744) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).
fof(i_0_2048,plain,
! [X4082,X4083,X4084] :
( ( c_Orderings_Oord__class_Oless__eq(X4084,X4083,X4082)
| ~ c_Orderings_Oord__class_Oless(X4084,X4083,X4082)
| ~ class_Orderings_Opreorder(X4084) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4084,X4082,X4083)
| ~ c_Orderings_Oord__class_Oless(X4084,X4083,X4082)
| ~ class_Orderings_Opreorder(X4084) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4084,X4083,X4082)
| c_Orderings_Oord__class_Oless__eq(X4084,X4082,X4083)
| c_Orderings_Oord__class_Oless(X4084,X4083,X4082)
| ~ class_Orderings_Opreorder(X4084) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1342])])]) ).
fof(i_0_2049,plain,
! [X4614,X4615,X4616] :
( ~ class_RealVector_Oreal__normed__algebra(X4616)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4616),X4615),c_Groups_Ouminus__class_Ouminus(X4616,X4614)) = c_Groups_Ouminus__class_Ouminus(X4616,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4616),X4615),X4614)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus])]) ).
fof(i_0_2050,plain,
! [X4611,X4612,X4613] :
( ~ class_RealVector_Oreal__normed__algebra(X4613)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4613),X4612),c_Groups_Ouminus__class_Ouminus(X4613,X4611)) = c_Groups_Ouminus__class_Ouminus(X4613,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4613),X4612),X4611)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right])]) ).
fof(i_0_2051,plain,
! [X4596,X4597,X4598] :
( ~ class_Rings_Oring(X4598)
| c_Groups_Ouminus__class_Ouminus(X4598,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),X4596)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),c_Groups_Ouminus__class_Ouminus(X4598,X4596)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).
cnf(i_0_2052,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[i_0_1343]) ).
fof(i_0_2053,plain,
! [X4584,X4585,X4586] :
( ~ class_Groups_Oordered__ab__group__add(X4586)
| ~ c_Orderings_Oord__class_Oless__eq(X4586,X4585,X4584)
| c_Orderings_Oord__class_Oless__eq(X4586,c_Groups_Ouminus__class_Ouminus(X4586,X4584),c_Groups_Ouminus__class_Ouminus(X4586,X4585)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).
cnf(i_0_2054,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1340]) ).
fof(i_0_2055,plain,
! [X4028] :
( ~ class_Rings_Olinordered__semidom(X4028)
| c_Orderings_Oord__class_Oless(X4028,c_Groups_Ozero__class_Ozero(X4028),c_Groups_Oplus__class_Oplus(X4028,c_Groups_Oone__class_Oone(X4028),c_Groups_Oone__class_Oone(X4028))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_2056,plain,
! [X5575] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5575,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5575))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__gt__diff__one]) ).
fof(i_0_2057,plain,
! [X4636,X4637,X4638] :
( ~ class_Groups_Ogroup__add(X4638)
| c_Groups_Oplus__class_Oplus(X4638,c_Groups_Ouminus__class_Ouminus(X4638,X4637),c_Groups_Oplus__class_Oplus(X4638,X4637,X4636)) = X4636 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).
fof(i_0_2058,plain,
! [X4749,X4750] :
( ( ~ c_Orderings_Oord__class_Oless(X4750,c_Groups_Ouminus__class_Ouminus(X4750,X4749),X4749)
| c_Orderings_Oord__class_Oless(X4750,c_Groups_Ozero__class_Ozero(X4750),X4749)
| ~ class_Groups_Olinordered__ab__group__add(X4750) )
& ( ~ c_Orderings_Oord__class_Oless(X4750,c_Groups_Ozero__class_Ozero(X4750),X4749)
| c_Orderings_Oord__class_Oless(X4750,c_Groups_Ouminus__class_Ouminus(X4750,X4749),X4749)
| ~ class_Groups_Olinordered__ab__group__add(X4750) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).
fof(i_0_2059,plain,
! [X4737,X4738] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4738,c_Groups_Ouminus__class_Ouminus(X4738,X4737),X4737)
| c_Orderings_Oord__class_Oless__eq(X4738,c_Groups_Ozero__class_Ozero(X4738),X4737)
| ~ class_Groups_Olinordered__ab__group__add(X4738) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4738,c_Groups_Ozero__class_Ozero(X4738),X4737)
| c_Orderings_Oord__class_Oless__eq(X4738,c_Groups_Ouminus__class_Ouminus(X4738,X4737),X4737)
| ~ class_Groups_Olinordered__ab__group__add(X4738) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).
fof(i_0_2060,plain,
! [X4751,X4752] :
( ( ~ c_Orderings_Oord__class_Oless(X4752,X4751,c_Groups_Ouminus__class_Ouminus(X4752,X4751))
| c_Orderings_Oord__class_Oless(X4752,X4751,c_Groups_Ozero__class_Ozero(X4752))
| ~ class_Rings_Olinordered__idom(X4752) )
& ( ~ c_Orderings_Oord__class_Oless(X4752,X4751,c_Groups_Ozero__class_Ozero(X4752))
| c_Orderings_Oord__class_Oless(X4752,X4751,c_Groups_Ouminus__class_Ouminus(X4752,X4751))
| ~ class_Rings_Olinordered__idom(X4752) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).
fof(i_0_2061,plain,
! [X4741,X4742] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4742,X4741,c_Groups_Ouminus__class_Ouminus(X4742,X4741))
| c_Orderings_Oord__class_Oless__eq(X4742,X4741,c_Groups_Ozero__class_Ozero(X4742))
| ~ class_Groups_Olinordered__ab__group__add(X4742) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4742,X4741,c_Groups_Ozero__class_Ozero(X4742))
| c_Orderings_Oord__class_Oless__eq(X4742,X4741,c_Groups_Ouminus__class_Ouminus(X4742,X4741))
| ~ class_Groups_Olinordered__ab__group__add(X4742) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).
fof(i_0_2062,plain,
! [X5534,X5535] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5535)),X5534) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5535),X5534)),
inference(variable_rename,[status(thm)],[fact_power__real__of__nat]) ).
fof(i_0_2063,plain,
! [X4958,X4959] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4959)),X4958) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4959),X4958)),
inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).
fof(i_0_2064,plain,
! [X5532,X5533] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5533),X5532)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5533)),X5532),
inference(variable_rename,[status(thm)],[fact_real__of__nat__power]) ).
cnf(i_0_2065,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1344]) ).
fof(i_0_2066,plain,
! [X4015,X4016,X4017] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4016,X4017)
| hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| X4017 = X4016
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4017,X4016) )
& ( ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| X4017 = X4016
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4017,X4016) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4016,X4017)
| hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4017,X4016) )
& ( ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4017,X4016) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4016,X4017)
| hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| X4017 = X4016
| ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017)) )
& ( ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| X4017 = X4016
| ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4016,X4017)
| hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017)) )
& ( ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017))
| ~ hBOOL(hAPP(hAPP(X4015,X4016),X4017)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_2067,plain,
! [X3629,X3630,X3631,X3632] :
( ~ class_Rings_Ocomm__semiring__0(X3632)
| c_Polynomial_Osmult(X3632,X3631,X3630) != c_Polynomial_OpCons(X3632,X3629,X3630)
| X3630 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3632)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique__lemma])]) ).
fof(i_0_2068,plain,
! [X4605,X4606,X4607] :
( ~ class_Rings_Oring(X4607)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4607),c_Groups_Ouminus__class_Ouminus(X4607,X4606)),c_Groups_Ouminus__class_Ouminus(X4607,X4605)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4607),X4606),X4605) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).
fof(i_0_2069,plain,
! [X4602,X4603,X4604] :
( ~ class_Rings_Oring(X4604)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4604),c_Groups_Ouminus__class_Ouminus(X4604,X4603)),X4602) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4604),X4603),c_Groups_Ouminus__class_Ouminus(X4604,X4602)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).
fof(i_0_2070,plain,
! [X5325,X5326,X5327] :
( ( ~ c_Rings_Odvd__class_Odvd(X5327,c_Groups_Ouminus__class_Ouminus(X5327,X5326),X5325)
| c_Rings_Odvd__class_Odvd(X5327,X5326,X5325)
| ~ class_Rings_Ocomm__ring__1(X5327) )
& ( ~ c_Rings_Odvd__class_Odvd(X5327,X5326,X5325)
| c_Rings_Odvd__class_Odvd(X5327,c_Groups_Ouminus__class_Ouminus(X5327,X5326),X5325)
| ~ class_Rings_Ocomm__ring__1(X5327) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff])])]) ).
fof(i_0_2071,plain,
! [X5328,X5329,X5330] :
( ( ~ c_Rings_Odvd__class_Odvd(X5330,X5329,c_Groups_Ouminus__class_Ouminus(X5330,X5328))
| c_Rings_Odvd__class_Odvd(X5330,X5329,X5328)
| ~ class_Rings_Ocomm__ring__1(X5330) )
& ( ~ c_Rings_Odvd__class_Odvd(X5330,X5329,X5328)
| c_Rings_Odvd__class_Odvd(X5330,X5329,c_Groups_Ouminus__class_Ouminus(X5330,X5328))
| ~ class_Rings_Ocomm__ring__1(X5330) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff])])]) ).
fof(i_0_2072,plain,
! [X4608,X4609,X4610] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4610),X4609),X4609) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4610),X4608),X4608)
| X4609 = X4608
| X4609 = c_Groups_Ouminus__class_Ouminus(X4610,X4608)
| ~ class_Rings_Oidom(X4610) )
& ( X4609 != X4608
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4610),X4609),X4609) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4610),X4608),X4608)
| ~ class_Rings_Oidom(X4610) )
& ( X4609 != c_Groups_Ouminus__class_Ouminus(X4610,X4608)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4610),X4609),X4609) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4610),X4608),X4608)
| ~ class_Rings_Oidom(X4610) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).
fof(i_0_2073,plain,
! [X4875,X4876,X4877] :
( ~ class_Rings_Olinordered__idom(X4877)
| ~ c_Polynomial_Opos__poly(X4877,X4876)
| ~ c_Polynomial_Opos__poly(X4877,X4875)
| c_Polynomial_Opos__poly(X4877,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4877),X4876,X4875)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__add])]) ).
fof(i_0_2074,plain,
! [X3396,X3397,X3398,X3399,X3400] :
( ( X3399 != X3398
| X3397 = X3396
| c_Groups_Ominus__class_Ominus(X3400,X3399,X3398) != c_Groups_Ominus__class_Ominus(X3400,X3397,X3396)
| ~ class_Groups_Oab__group__add(X3400) )
& ( X3397 != X3396
| X3399 = X3398
| c_Groups_Ominus__class_Ominus(X3400,X3399,X3398) != c_Groups_Ominus__class_Ominus(X3400,X3397,X3396)
| ~ class_Groups_Oab__group__add(X3400) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).
cnf(i_0_2075,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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_1321]) ).
cnf(i_0_2076,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) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1322]) ).
fof(i_0_2077,plain,
! [X5561,X5562] :
( X5562 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5562))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5562),X5561)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X5562)),X5561) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__power])]) ).
fof(i_0_2078,plain,
! [X4055,X4056,X4057] :
( ( c_Orderings_Oord__class_Oless(X4057,X4056,X4055)
| X4056 = X4055
| ~ c_Orderings_Oord__class_Oless__eq(X4057,X4056,X4055)
| ~ class_Orderings_Olinorder(X4057) )
& ( X4056 != X4055
| ~ c_Orderings_Oord__class_Oless(X4057,X4056,X4055)
| ~ c_Orderings_Oord__class_Oless__eq(X4057,X4056,X4055)
| ~ class_Orderings_Olinorder(X4057) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1345])])]) ).
fof(i_0_2079,plain,
! [X4639,X4640,X4641] :
( ~ class_Groups_Oab__group__add(X4641)
| c_Groups_Ouminus__class_Ouminus(X4641,c_Groups_Ominus__class_Ominus(X4641,X4640,X4639)) = c_Groups_Ominus__class_Ominus(X4641,X4639,X4640) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).
fof(i_0_2080,plain,
! [X3071,X3072,X3073] :
( ( c_Orderings_Oord__class_Oless__eq(X3073,X3072,X3071)
| X3072 != X3071
| ~ class_Orderings_Oorder(X3073) )
& ( c_Orderings_Oord__class_Oless__eq(X3073,X3071,X3072)
| X3072 != X3071
| ~ class_Orderings_Oorder(X3073) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3073,X3072,X3071)
| ~ c_Orderings_Oord__class_Oless__eq(X3073,X3071,X3072)
| X3072 = X3071
| ~ class_Orderings_Oorder(X3073) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_2081,plain,
! [X3060,X3061,X3062] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3062,X3060,X3061)
| X3060 = X3061
| ~ c_Orderings_Oord__class_Oless__eq(X3062,X3061,X3060)
| ~ class_Orderings_Oorder(X3062) )
& ( X3060 != X3061
| c_Orderings_Oord__class_Oless__eq(X3062,X3060,X3061)
| ~ c_Orderings_Oord__class_Oless__eq(X3062,X3061,X3060)
| ~ class_Orderings_Oorder(X3062) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_2082,plain,
! [X3041,X3042,X3043] :
( ~ class_Orderings_Oorder(X3043)
| ~ c_Orderings_Oord__class_Oless__eq(X3043,X3042,X3041)
| ~ c_Orderings_Oord__class_Oless__eq(X3043,X3041,X3042)
| X3042 = X3041 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_2083,plain,
! [X3034,X3035,X3036] :
( ~ class_Orderings_Oorder(X3036)
| ~ c_Orderings_Oord__class_Oless__eq(X3036,X3035,X3034)
| ~ c_Orderings_Oord__class_Oless__eq(X3036,X3034,X3035)
| X3034 = X3035 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_2084,plain,
! [X5563] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5563))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5563) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5563)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5563)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff])]) ).
fof(i_0_2085,plain,
! [X3938,X3939] :
( ~ class_Rings_Olinordered__semidom(X3939)
| c_Orderings_Oord__class_Oless(X3939,X3938,c_Groups_Oplus__class_Oplus(X3939,X3938,c_Groups_Oone__class_Oone(X3939))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_2086,plain,
! [X3117,X3118,X3119,X3120,X3121] :
( ( X3120 = X3118
| c_Polynomial_OpCons(X3121,X3120,X3119) != c_Polynomial_OpCons(X3121,X3118,X3117)
| ~ class_Groups_Ozero(X3121) )
& ( X3119 = X3117
| c_Polynomial_OpCons(X3121,X3120,X3119) != c_Polynomial_OpCons(X3121,X3118,X3117)
| ~ class_Groups_Ozero(X3121) )
& ( X3120 != X3118
| X3119 != X3117
| c_Polynomial_OpCons(X3121,X3120,X3119) = c_Polynomial_OpCons(X3121,X3118,X3117)
| ~ class_Groups_Ozero(X3121) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff])])]) ).
fof(i_0_2087,plain,
! [X3405,X3406,X3407,X3408] :
( ( c_Polynomial_Omonom(X3408,X3407,X3406) != c_Polynomial_Omonom(X3408,X3405,X3406)
| X3407 = X3405
| ~ class_Groups_Ozero(X3408) )
& ( X3407 != X3405
| c_Polynomial_Omonom(X3408,X3407,X3406) = c_Polynomial_Omonom(X3408,X3405,X3406)
| ~ class_Groups_Ozero(X3408) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__iff])])]) ).
fof(i_0_2088,plain,
! [X3097,X3098,X3099,X3100] :
( ( c_Groups_Oplus__class_Oplus(X3100,X3099,X3098) != c_Groups_Oplus__class_Oplus(X3100,X3097,X3098)
| X3099 = X3097
| ~ class_Groups_Ocancel__semigroup__add(X3100) )
& ( X3099 != X3097
| c_Groups_Oplus__class_Oplus(X3100,X3099,X3098) = c_Groups_Oplus__class_Oplus(X3100,X3097,X3098)
| ~ class_Groups_Ocancel__semigroup__add(X3100) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_2089,plain,
! [X3085,X3086,X3087,X3088] :
( ~ class_Groups_Ocancel__semigroup__add(X3088)
| c_Groups_Oplus__class_Oplus(X3088,X3087,X3086) != c_Groups_Oplus__class_Oplus(X3088,X3085,X3086)
| X3087 = X3085 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_2090,plain,
! [X3089,X3090,X3091,X3092] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3092)
| c_Groups_Oplus__class_Oplus(X3092,X3091,X3090) != c_Groups_Oplus__class_Oplus(X3092,X3091,X3089)
| X3090 = X3089 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_2091,plain,
! [X3101,X3102,X3103,X3104] :
( ( c_Groups_Oplus__class_Oplus(X3104,X3103,X3102) != c_Groups_Oplus__class_Oplus(X3104,X3103,X3101)
| X3102 = X3101
| ~ class_Groups_Ocancel__semigroup__add(X3104) )
& ( X3102 != X3101
| c_Groups_Oplus__class_Oplus(X3104,X3103,X3102) = c_Groups_Oplus__class_Oplus(X3104,X3103,X3101)
| ~ class_Groups_Ocancel__semigroup__add(X3104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_2092,plain,
! [X3093,X3094,X3095,X3096] :
( ~ class_Groups_Ocancel__semigroup__add(X3096)
| c_Groups_Oplus__class_Oplus(X3096,X3095,X3094) != c_Groups_Oplus__class_Oplus(X3096,X3095,X3093)
| X3094 = X3093 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_2093,plain,
! [X3974,X3975,X3976] :
( ~ class_Orderings_Oorder(X3976)
| ~ c_Orderings_Oord__class_Oless(X3976,X3975,X3974)
| ~ c_Orderings_Oord__class_Oless(X3976,X3974,X3975) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1346])]) ).
fof(i_0_2094,plain,
! [X4006,X4007,X4008] :
( ( c_Orderings_Oord__class_Oless(X4008,X4007,X4006)
| c_Orderings_Oord__class_Oless(X4008,X4006,X4007)
| X4007 = X4006
| ~ class_Orderings_Olinorder(X4008) )
& ( ~ c_Orderings_Oord__class_Oless(X4008,X4006,X4007)
| ~ c_Orderings_Oord__class_Oless(X4008,X4007,X4006)
| ~ class_Orderings_Olinorder(X4008) )
& ( X4007 != X4006
| ~ c_Orderings_Oord__class_Oless(X4008,X4007,X4006)
| ~ class_Orderings_Olinorder(X4008) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1347])])]) ).
fof(i_0_2095,plain,
! [X4094,X4095,X4096] :
( ( c_Orderings_Oord__class_Oless(X4096,X4095,X4094)
| c_Orderings_Oord__class_Oless__eq(X4096,X4094,X4095)
| ~ class_Orderings_Olinorder(X4096) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4096,X4094,X4095)
| ~ c_Orderings_Oord__class_Oless(X4096,X4095,X4094)
| ~ class_Orderings_Olinorder(X4096) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1348])])]) ).
fof(i_0_2096,plain,
! [X4061,X4062,X4063] :
( ~ class_Orderings_Olinorder(X4063)
| ~ c_Orderings_Oord__class_Oless__eq(X4063,X4062,X4061)
| ~ c_Orderings_Oord__class_Oless(X4063,X4061,X4062) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1349])]) ).
fof(i_0_2097,plain,
! [X4091,X4092,X4093] :
( ( c_Orderings_Oord__class_Oless__eq(X4093,X4092,X4091)
| c_Orderings_Oord__class_Oless(X4093,X4091,X4092)
| ~ class_Orderings_Olinorder(X4093) )
& ( ~ c_Orderings_Oord__class_Oless(X4093,X4091,X4092)
| ~ c_Orderings_Oord__class_Oless__eq(X4093,X4092,X4091)
| ~ class_Orderings_Olinorder(X4093) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1350])])]) ).
fof(i_0_2098,plain,
! [X3989,X3990,X3991] :
( ~ class_Orderings_Opreorder(X3991)
| ~ c_Orderings_Oord__class_Oless(X3991,X3990,X3989)
| ~ c_Orderings_Oord__class_Oless(X3991,X3989,X3990) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1351])]) ).
fof(i_0_2099,plain,
! [X3986,X3987,X3988] :
( ~ class_Orderings_Opreorder(X3988)
| ~ c_Orderings_Oord__class_Oless(X3988,X3987,X3986)
| ~ c_Orderings_Oord__class_Oless(X3988,X3986,X3987) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1352])]) ).
fof(i_0_2100,plain,
! [X3977,X3978,X3979] :
( ~ class_Orderings_Opreorder(X3979)
| ~ c_Orderings_Oord__class_Oless(X3979,X3978,X3977)
| ~ c_Orderings_Oord__class_Oless(X3979,X3977,X3978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1353])]) ).
fof(i_0_2101,plain,
! [X3947,X3948,X3949] :
( ~ class_Orderings_Opreorder(X3949)
| ~ c_Orderings_Oord__class_Oless(X3949,X3948,X3947)
| ~ c_Orderings_Oord__class_Oless(X3949,X3947,X3948) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1354])]) ).
fof(i_0_2102,plain,
! [X5553,X5554] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5554,c_RealDef_Oreal(tc_Nat_Onat,X5553))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5554),X5553) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le])]) ).
fof(i_0_2103,plain,
! [X5555,X5556] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5556),X5555)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5556,c_RComplete_Onatfloor(X5555)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor])]) ).
cnf(i_0_2104,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1355]) ).
cnf(i_0_2105,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1356]) ).
fof(i_0_2106,plain,
! [X3133,X3134,X3135] :
( ( hAPP(c_Polynomial_Opoly(X3135,X3134),X3133) != c_Groups_Ozero__class_Ozero(X3135)
| X3134 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3135))
| c_Polynomial_Oorder(X3135,X3133,X3134) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X3135) )
& ( X3134 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3135))
| hAPP(c_Polynomial_Opoly(X3135,X3134),X3133) = c_Groups_Ozero__class_Ozero(X3135)
| ~ class_Rings_Oidom(X3135) )
& ( c_Polynomial_Oorder(X3135,X3133,X3134) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X3135,X3134),X3133) = c_Groups_Ozero__class_Ozero(X3135)
| ~ class_Rings_Oidom(X3135) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__root])])]) ).
fof(i_0_2107,plain,
! [X3473,X3474] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3474,X3473) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3473,X3474) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3474 = X3473 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).
fof(i_0_2108,plain,
! [X5557] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5557)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5557)),X5557) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__natfloor__le])]) ).
cnf(i_0_2109,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,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_1325]) ).
fof(i_0_2110,plain,
! [X5402,X5403] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5403,X5402)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5403),X5402) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5403),X5402)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5403,X5402) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I1_J])]) ).
fof(i_0_2111,plain,
! [X5400,X5401] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5401,X5400)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5401,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5400)) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5401,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5400))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5401,X5400) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I2_J])]) ).
fof(i_0_2112,plain,
! [X3698,X3699] :
( ~ class_Rings_Olinordered__ring(X3699)
| c_Orderings_Oord__class_Oless__eq(X3699,c_Groups_Ozero__class_Ozero(X3699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3699),X3698),X3698)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).
fof(i_0_2113,plain,
! [X5461,X5462] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5462,X5461)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5461,X5462)
| X5462 = X5461 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym])]) ).
fof(i_0_2114,plain,
! [X5459,X5460] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5460,X5459)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5459,X5460)
| X5460 = X5459 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__antisym])]) ).
fof(i_0_2115,plain,
! [X5451,X5452] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5452,X5451)
| X5452 = X5451
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5452,X5451) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5451,X5452)
| X5452 = X5451
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5452,X5451) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1357])])]) ).
fof(i_0_2116,plain,
! [X5449,X5450] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5450,X5449)
| X5450 = X5449
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5450,X5449) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5449,X5450)
| X5450 = X5449
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5450,X5449) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1358])])]) ).
fof(i_0_2117,plain,
! [X5447,X5448] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5447,X5448)
| X5447 = X5448
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5448,X5447) )
& ( X5447 != X5448
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5447,X5448)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5448,X5447) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv])])]) ).
fof(i_0_2118,plain,
! [X5443,X5444] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5444,X5443)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5444,X5443)
| X5444 = X5443 )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5443,X5444)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5444,X5443)
| X5444 = X5443 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1359])])]) ).
fof(i_0_2119,plain,
! [X5441,X5442] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5442,X5441)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5442,X5441)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5441,X5442) )
& ( X5442 != X5441
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5442,X5441)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5441,X5442) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5442,X5441)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5442,X5441)
| X5442 = X5441 )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5441,X5442)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5442,X5441)
| X5442 = X5441 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1360])])]) ).
fof(i_0_2120,plain,
! [X5439,X5440] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5440,X5439)
| X5440 = X5439
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5440,X5439) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5439,X5440)
| X5440 = X5439
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5440,X5439) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5440,X5439)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5439,X5440)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5440,X5439) )
& ( X5440 != X5439
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5440,X5439) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1361])])]) ).
fof(i_0_2121,plain,
! [X5437,X5438] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5438,X5437)
| X5438 != X5437 )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5437,X5438)
| X5438 != X5437 )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5438,X5437)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5437,X5438)
| X5438 = X5437 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff])])]) ).
fof(i_0_2122,plain,
! [X5171,X5172] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5172,X5171)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5171,X5172)
| X5172 = X5171 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).
fof(i_0_2123,plain,
! [X3324,X3325] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3325,X3324)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3324,X3325)
| X3325 = X3324 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_2124,plain,
! [X3109,X3110] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3110,X3109)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3109,X3110)
| X3110 = X3109 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
fof(i_0_2125,plain,
! [X3519,X3520,X3521] :
( ~ class_Groups_Ogroup__add(X3521)
| c_Groups_Ominus__class_Ominus(X3521,c_Groups_Oplus__class_Oplus(X3521,X3520,X3519),X3519) = X3520 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(i_0_2126,plain,
! [X3522,X3523,X3524] :
( ~ class_Groups_Ogroup__add(X3524)
| c_Groups_Oplus__class_Oplus(X3524,c_Groups_Ominus__class_Ominus(X3524,X3523,X3522),X3522) = X3523 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
cnf(i_0_2127,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(split_conjunct,[status(thm)],[i_0_1362]) ).
fof(i_0_2128,plain,
! [X4951,X4952] :
( ( X4952 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4952),X4951) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4952) )
& ( X4951 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4952),X4951) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4952) )
& ( X4952 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X4951 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4952),X4951) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4952) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
cnf(i_0_2129,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1288]) ).
fof(i_0_2130,plain,
! [X3724,X3725,X3726] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3726,X3725) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3724,X3725)
| X3726 = X3724 )
& ( X3726 != X3724
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3726,X3725) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3724,X3725) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_2131,plain,
! [X3721,X3722,X3723] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3723,X3722) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3723,X3721)
| X3722 = X3721 )
& ( X3722 != X3721
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3723,X3722) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3723,X3721) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
cnf(i_0_2132,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_1363]) ).
cnf(i_0_2133,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1307]) ).
cnf(i_0_2134,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1364]) ).
fof(i_0_2135,plain,
! [X5247,X5248,X5249] :
( ~ class_Rings_Ocomm__semiring__1(X5249)
| c_Rings_Odvd__class_Odvd(X5249,X5248,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5249),X5248),X5247)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__left])]) ).
fof(i_0_2136,plain,
! [X5250,X5251,X5252] :
( ~ class_Rings_Ocomm__semiring__1(X5252)
| c_Rings_Odvd__class_Odvd(X5252,X5251,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5250),X5251)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__right])]) ).
fof(i_0_2137,plain,
! [X3752,X3753,X3755,X3756,X3757] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3753,X3752)
| X3752 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3753,esk6_2(X3752,X3753)) )
& ( X3755 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3756,X3757)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3756,X3755) ) ),
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__Suc__ex__iff])])])])]) ).
fof(i_0_2138,plain,
! [X3249,X3250,X3252,X3253,X3254] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3250,X3249)
| X3249 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3250,esk5_2(X3249,X3250)) )
& ( X3252 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3253,X3254)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3253,X3252) ) ),
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])])])])]) ).
cnf(i_0_2139,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1365]) ).
fof(i_0_2140,plain,
! [X3479,X3480] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3480,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3480,X3479)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(i_0_2141,plain,
! [X3710,X3711] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3711,X3710),X3711) = X3710,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
fof(i_0_2142,plain,
! [X3708,X3709] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3709,X3708),X3708) = X3709,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).
fof(i_0_2143,plain,
! [X3247,X3248] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3248,X3247),X3248),
inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).
fof(i_0_2144,plain,
! [X3244,X3245] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3245,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3245,X3244)),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_2145,plain,
! [X3242,X3243] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3243,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3242,X3243)),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_2146,plain,
! [X4725] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X4725))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4725) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4725)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X4725)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])]) ).
fof(i_0_2147,plain,
! [X5222] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5222),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5222,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5222,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5222),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one])]) ).
cnf(i_0_2148,plain,
( X1 = c_Nat_OSuc(esk16_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_1366]) ).
fof(i_0_2149,plain,
! [X3488,X3489,X3490] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3490),X3489) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3488),X3489)
| X3490 = X3488
| X3489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3490 != X3488
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3490),X3489) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3488),X3489) )
& ( X3489 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3490),X3489) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3488),X3489) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_2150,plain,
! [X3583,X3584,X3585] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3584),X3585) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3583),X3585)
| X3584 = X3583
| X3585 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3584 != X3583
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3584),X3585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3583),X3585)
| X3585 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__right__cancel])])]) ).
fof(i_0_2151,plain,
! [X3877,X3878,X3879] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3879),X3878) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3879),X3877)
| X3879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3878 = X3877 )
& ( X3879 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3879),X3878) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3879),X3877) )
& ( X3878 != X3877
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3879),X3878) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3879),X3877) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_2152,plain,
! [X3491,X3492,X3493] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3493),X3492) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3493),X3491)
| X3492 = X3491
| X3493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3492 != X3491
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3493),X3492) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3493),X3491) )
& ( X3493 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3493),X3492) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3493),X3491) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_2153,plain,
! [X3580,X3581,X3582] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3582),X3581) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3582),X3580)
| X3581 = X3580
| X3582 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3581 != X3580
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3582),X3581) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3582),X3580)
| X3582 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__left__cancel])])]) ).
fof(i_0_2154,plain,
! [X5582,X5583] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5583,X5582)
| c_Nat__Transfer_Otsub(X5582,X5583) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5582,X5583) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).
fof(i_0_2155,plain,
! [X5527,X5528] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5528,X5527)
| c_Nat__Transfer_Otsub(X5527,X5528) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5527,X5528) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5528,X5527)
| c_Nat__Transfer_Otsub(X5527,X5528) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1367])]) ).
fof(i_0_2156,plain,
! [X4085,X4086,X4087] :
( ( c_Orderings_Oord__class_Oless__eq(X4087,X4086,X4085)
| ~ c_Orderings_Oord__class_Oless(X4087,X4086,X4085)
| ~ class_Orderings_Oorder(X4087) )
& ( X4086 != X4085
| ~ c_Orderings_Oord__class_Oless(X4087,X4086,X4085)
| ~ class_Orderings_Oorder(X4087) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4087,X4086,X4085)
| X4086 = X4085
| c_Orderings_Oord__class_Oless(X4087,X4086,X4085)
| ~ class_Orderings_Oorder(X4087) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_2157,plain,
! [X4079,X4080,X4081] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4081,X4080,X4079)
| c_Orderings_Oord__class_Oless(X4081,X4080,X4079)
| X4080 = X4079
| ~ class_Orderings_Oorder(X4081) )
& ( ~ c_Orderings_Oord__class_Oless(X4081,X4080,X4079)
| c_Orderings_Oord__class_Oless__eq(X4081,X4080,X4079)
| ~ class_Orderings_Oorder(X4081) )
& ( X4080 != X4079
| c_Orderings_Oord__class_Oless__eq(X4081,X4080,X4079)
| ~ class_Orderings_Oorder(X4081) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_2158,plain,
! [X4067,X4068,X4069] :
( ~ class_Orderings_Oorder(X4069)
| X4068 = X4067
| ~ c_Orderings_Oord__class_Oless__eq(X4069,X4068,X4067)
| c_Orderings_Oord__class_Oless(X4069,X4068,X4067) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_2159,plain,
! [X4052,X4053,X4054] :
( ~ class_Orderings_Oorder(X4054)
| ~ c_Orderings_Oord__class_Oless__eq(X4054,X4053,X4052)
| c_Orderings_Oord__class_Oless(X4054,X4053,X4052)
| X4053 = X4052 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_2160,plain,
! [X4049,X4050,X4051] :
( ~ class_Orderings_Oorder(X4051)
| ~ c_Orderings_Oord__class_Oless__eq(X4051,X4050,X4049)
| X4050 = X4049
| c_Orderings_Oord__class_Oless(X4051,X4050,X4049) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_2161,plain,
! [X4046,X4047,X4048] :
( ~ class_Orderings_Oorder(X4048)
| ~ c_Orderings_Oord__class_Oless__eq(X4048,X4047,X4046)
| X4046 = X4047
| c_Orderings_Oord__class_Oless(X4048,X4047,X4046) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_2162,plain,
! [X4070,X4071,X4072] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4072,X4071,X4070)
| X4071 = X4070
| c_Orderings_Oord__class_Oless(X4072,X4071,X4070)
| ~ class_Orderings_Olinorder(X4072) )
& ( X4071 != X4070
| c_Orderings_Oord__class_Oless__eq(X4072,X4071,X4070)
| c_Orderings_Oord__class_Oless(X4072,X4071,X4070)
| ~ class_Orderings_Olinorder(X4072) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1368])])]) ).
fof(i_0_2163,plain,
! [X4064,X4065,X4066] :
( ~ class_Orderings_Oorder(X4066)
| X4065 = X4064
| ~ c_Orderings_Oord__class_Oless__eq(X4066,X4064,X4065)
| c_Orderings_Oord__class_Oless(X4066,X4064,X4065) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_2164,plain,
! [X4772,X4773] :
( ~ class_Rings_Ocomm__ring__1(X4773)
| c_Groups_Ouminus__class_Ouminus(X4773,X4772) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4773),c_Groups_Ouminus__class_Ouminus(X4773,c_Groups_Oone__class_Oone(X4773))),X4772) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).
fof(i_0_2165,plain,
! [X5210,X5211] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5211,X5210)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5211),c_RComplete_Onatceiling(X5210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__mono])]) ).
fof(i_0_2166,plain,
! [X4732,X4733] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4733,X4732)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X4733),c_RComplete_Onatfloor(X4732)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__mono])]) ).
fof(i_0_2167,plain,
! [X4058,X4059,X4060] :
( ~ class_Orderings_Opreorder(X4060)
| ~ c_Orderings_Oord__class_Oless(X4060,X4059,X4058)
| c_Orderings_Oord__class_Oless__eq(X4060,X4059,X4058) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
cnf(i_0_2168,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1366]) ).
fof(i_0_2169,plain,
! [X5266,X5267,X5268,X5269] :
( ~ class_Rings_Odvd(X5269)
| X5268 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5269),X5267),X5266)
| c_Rings_Odvd__class_Odvd(X5269,X5267,X5268) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvdI])]) ).
fof(i_0_2170,plain,
! [X5136] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5136)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5136) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5136)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5136) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).
fof(i_0_2171,plain,
! [X4902,X4903] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4903,X4902))
| X4902 != c_Groups_Ozero__class_Ozero(X4903)
| ~ class_RealVector_Oreal__normed__vector(X4903) )
& ( X4902 = c_Groups_Ozero__class_Ozero(X4903)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4903,X4902))
| ~ class_RealVector_Oreal__normed__vector(X4903) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).
fof(i_0_2172,plain,
! [X4874] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4874)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4874)),
inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(i_0_2173,plain,
! [X3241] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3241,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3241),X3241)),
inference(variable_rename,[status(thm)],[fact_le__square]) ).
fof(i_0_2174,plain,
! [X4780,X4781,X4782] :
( ~ class_Groups_Ogroup__add(X4782)
| c_Groups_Ominus__class_Ominus(X4782,X4781,c_Groups_Ouminus__class_Ouminus(X4782,X4780)) = c_Groups_Oplus__class_Oplus(X4782,X4781,X4780) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).
fof(i_0_2175,plain,
! [X4783,X4784,X4785] :
( ~ class_Rings_Ocomm__ring__1(X4785)
| c_Groups_Ominus__class_Ominus(X4785,X4784,X4783) = c_Groups_Oplus__class_Oplus(X4785,X4784,c_Groups_Ouminus__class_Ouminus(X4785,X4783)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).
fof(i_0_2176,plain,
! [X4774,X4775,X4776] :
( ~ class_Groups_Ogroup__add(X4776)
| c_Groups_Ominus__class_Ominus(X4776,X4775,X4774) = c_Groups_Oplus__class_Oplus(X4776,X4775,c_Groups_Ouminus__class_Ouminus(X4776,X4774)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).
fof(i_0_2177,plain,
! [X4777,X4778,X4779] :
( ~ class_Groups_Oab__group__add(X4779)
| c_Groups_Ominus__class_Ominus(X4779,X4778,X4777) = c_Groups_Oplus__class_Oplus(X4779,X4778,c_Groups_Ouminus__class_Ouminus(X4779,X4777)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).
fof(i_0_2178,plain,
! [X2997,X2998] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2998,X2997),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X2997 = c_Groups_Ozero__class_Ozero(X2998)
| ~ class_RealVector_Oreal__normed__vector(X2998) )
& ( X2997 != c_Groups_Ozero__class_Ozero(X2998)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2998,X2997),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X2998) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])]) ).
fof(i_0_2179,plain,
! [X3477,X3478] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3478,X3477) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3478,X3477) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3478,X3477)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3478,X3477) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])]) ).
fof(i_0_2180,plain,
! [X5134,X5135] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5135,X5134)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5135,X5134) )
& ( X5135 != X5134
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5135,X5134) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5135,X5134)
| X5135 = X5134
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5135,X5134) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
fof(i_0_2181,plain,
! [X4190,X4191] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4191,X4190)
| X4191 = X4190
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4191,X4190) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_2182,plain,
! [X4186,X4187] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4187,X4186)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4187,X4186)
| X4187 = X4186 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4187,X4186)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4187,X4186) )
& ( X4187 != X4186
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4187,X4186) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_2183,plain,
! [X4184,X4185] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4185,X4184)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4185,X4184) )
& ( X4185 != X4184
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4185,X4184) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4185,X4184)
| X4185 = X4184
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4185,X4184) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_2184,plain,
! [X4714,X4715] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4715,X4714)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4715,X4714)
| X4715 = X4714 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4715,X4714)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4715,X4714) )
& ( X4715 != X4714
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4715,X4714) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(i_0_2185,plain,
! [X4712,X4713] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4713,X4712)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4713,X4712) )
& ( X4713 != X4712
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4713,X4712) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4713,X4712)
| X4713 = X4712
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4713,X4712) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
fof(i_0_2186,plain,
! [X3475,X3476] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3476,X3475)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3476,X3475) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H])]) ).
fof(i_0_2187,plain,
! [X5324] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X5324)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X5324),
inference(variable_rename,[status(thm)],[fact_complex__i__mult__minus]) ).
fof(i_0_2188,plain,
! [X3220,X3221] :
( ~ class_Groups_Ozero(X3221)
| c_Polynomial_Omonom(X3221,X3220,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X3221,X3220,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3221))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__0])]) ).
fof(i_0_2189,plain,
! [X4194,X4195] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4195,X4194)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4195,X4194) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_2190,plain,
! [X4192,X4193] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4193,X4192)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4193,X4192) )
& ( X4193 != X4192
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4193,X4192) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_2191,plain,
! [X4188,X4189] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4189,X4188)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4189,X4188) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_2192,plain,
! [X4872,X4873] :
( ~ class_RealVector_Oreal__normed__vector(X4873)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4873,X4872),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1369])]) ).
cnf(i_0_2193,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__one]) ).
fof(i_0_2194,plain,
! [X3591,X3592] :
( ~ class_Rings_Ocomm__semiring__0(X3592)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3592)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3592))),X3591) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3592)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__left])]) ).
fof(i_0_2195,plain,
! [X5141,X5142] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5142,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5141)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5142,X5141),
inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(i_0_2196,plain,
! [X5143,X5144] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5144,X5143) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5144,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5143)),
inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).
fof(i_0_2197,plain,
! [X4862,X4863] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4863,X4862) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4863,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4862)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
fof(i_0_2198,plain,
! [X4860,X4861] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4861,X4860) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4861,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4860)),
inference(variable_rename,[status(thm)],[fact_real__diff__def]) ).
fof(i_0_2199,plain,
! [X4729,X4730] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4730,X4729) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X4730,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X4729)),
inference(variable_rename,[status(thm)],[fact_complex__diff__def]) ).
fof(i_0_2200,plain,
! [X5536] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5536),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X5536 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5536 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5536),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__zero__cancel__iff])]) ).
fof(i_0_2201,plain,
! [X2927,X2928] :
( hAPP(X2928,esk1_2(X2927,X2928)) != hAPP(X2927,esk1_2(X2927,X2928))
| X2928 = X2927 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_2202,plain,
! [X3624,X3625,X3626] :
( ( c_Polynomial_Osmult(X3626,X3625,X3624) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3626))
| X3625 = c_Groups_Ozero__class_Ozero(X3626)
| X3624 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3626))
| ~ class_Rings_Oidom(X3626) )
& ( X3625 != c_Groups_Ozero__class_Ozero(X3626)
| c_Polynomial_Osmult(X3626,X3625,X3624) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3626))
| ~ class_Rings_Oidom(X3626) )
& ( X3624 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3626))
| c_Polynomial_Osmult(X3626,X3625,X3624) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3626))
| ~ class_Rings_Oidom(X3626) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__eq__0__iff])])]) ).
fof(i_0_2203,plain,
! [X4810,X4811] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4811,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4810)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X4811 = X4810 )
& ( X4811 != X4810
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4811,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4810)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff])]) ).
fof(i_0_2204,plain,
! [X5552] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5552),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[i_0_1370]) ).
fof(i_0_2205,plain,
! [X5016,X5017,X5018] :
( ( X5017 = c_Groups_Ozero__class_Ozero(X5018)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5018),X5017),X5016) != c_Groups_Ozero__class_Ozero(X5018)
| ~ class_Power_Opower(X5018)
| ~ class_Rings_Omult__zero(X5018)
| ~ class_Rings_Ono__zero__divisors(X5018)
| ~ class_Rings_Ozero__neq__one(X5018) )
& ( X5016 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5018),X5017),X5016) != c_Groups_Ozero__class_Ozero(X5018)
| ~ class_Power_Opower(X5018)
| ~ class_Rings_Omult__zero(X5018)
| ~ class_Rings_Ono__zero__divisors(X5018)
| ~ class_Rings_Ozero__neq__one(X5018) )
& ( X5017 != c_Groups_Ozero__class_Ozero(X5018)
| X5016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5018),X5017),X5016) = c_Groups_Ozero__class_Ozero(X5018)
| ~ class_Power_Opower(X5018)
| ~ class_Rings_Omult__zero(X5018)
| ~ class_Rings_Ono__zero__divisors(X5018)
| ~ class_Rings_Ozero__neq__one(X5018) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_2206,plain,
! [X4770,X4771] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4771),X4770),X4770) != c_Groups_Oone__class_Oone(X4771)
| X4770 = c_Groups_Oone__class_Oone(X4771)
| X4770 = c_Groups_Ouminus__class_Ouminus(X4771,c_Groups_Oone__class_Oone(X4771))
| ~ class_Rings_Oring__1__no__zero__divisors(X4771) )
& ( X4770 != c_Groups_Oone__class_Oone(X4771)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4771),X4770),X4770) = c_Groups_Oone__class_Oone(X4771)
| ~ class_Rings_Oring__1__no__zero__divisors(X4771) )
& ( X4770 != c_Groups_Ouminus__class_Ouminus(X4771,c_Groups_Oone__class_Oone(X4771))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4771),X4770),X4770) = c_Groups_Oone__class_Oone(X4771)
| ~ class_Rings_Oring__1__no__zero__divisors(X4771) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).
fof(i_0_2207,plain,
! [X2984,X2985,X2986] :
( ( X2985 = c_Groups_Ozero__class_Ozero(X2986)
| c_Polynomial_OpCons(X2986,X2985,X2984) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2986))
| ~ class_Groups_Ozero(X2986) )
& ( X2984 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2986))
| c_Polynomial_OpCons(X2986,X2985,X2984) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2986))
| ~ class_Groups_Ozero(X2986) )
& ( X2985 != c_Groups_Ozero__class_Ozero(X2986)
| X2984 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2986))
| c_Polynomial_OpCons(X2986,X2985,X2984) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2986))
| ~ class_Groups_Ozero(X2986) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff])])]) ).
fof(i_0_2208,plain,
! [X3180,X3181,X3182] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3182,X3181,X3180) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3182))
| X3181 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3182))
| ~ class_Rings_Ocomm__semiring__0(X3182) )
& ( X3181 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3182))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3182,X3181,X3180) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3182))
| ~ class_Rings_Ocomm__semiring__0(X3182) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__iff])])]) ).
fof(i_0_2209,plain,
! [X4009,X4010,X4011] :
( ( X4010 = X4009
| c_Orderings_Oord__class_Oless(X4011,X4010,X4009)
| c_Orderings_Oord__class_Oless(X4011,X4009,X4010)
| ~ class_Orderings_Olinorder(X4011) )
& ( ~ c_Orderings_Oord__class_Oless(X4011,X4010,X4009)
| X4010 != X4009
| ~ class_Orderings_Olinorder(X4011) )
& ( ~ c_Orderings_Oord__class_Oless(X4011,X4009,X4010)
| X4010 != X4009
| ~ class_Orderings_Olinorder(X4011) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_2210,plain,
! [X3935,X3936,X3937] :
( ~ class_Rings_Olinordered__idom(X3937)
| X3936 = X3935
| c_Orderings_Oord__class_Oless(X3937,X3936,X3935)
| c_Orderings_Oord__class_Oless(X3937,X3935,X3936) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1371])]) ).
fof(i_0_2211,plain,
! [X4001,X4002,X4003] :
( ~ class_Orderings_Olinorder(X4003)
| c_Orderings_Oord__class_Oless(X4003,X4002,X4001)
| X4002 = X4001
| c_Orderings_Oord__class_Oless(X4003,X4001,X4002) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_2212,plain,
! [X3998,X3999,X4000] :
( ( c_Orderings_Oord__class_Oless(X4000,X3998,X3999)
| X3998 = X3999
| c_Orderings_Oord__class_Oless(X4000,X3999,X3998)
| ~ class_Orderings_Olinorder(X4000) )
& ( X3998 != X3999
| ~ c_Orderings_Oord__class_Oless(X4000,X3998,X3999)
| c_Orderings_Oord__class_Oless(X4000,X3999,X3998)
| ~ class_Orderings_Olinorder(X4000) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1372])])]) ).
fof(i_0_2213,plain,
! [X3995,X3996,X3997] :
( ~ class_Orderings_Olinorder(X3997)
| X3996 = X3995
| c_Orderings_Oord__class_Oless(X3997,X3996,X3995)
| c_Orderings_Oord__class_Oless(X3997,X3995,X3996) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1373])]) ).
fof(i_0_2214,plain,
! [X3944,X3945,X3946] :
( ~ class_Orderings_Olinorder(X3946)
| c_Orderings_Oord__class_Oless(X3946,X3945,X3944)
| X3945 = X3944
| c_Orderings_Oord__class_Oless(X3946,X3944,X3945) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1374])]) ).
fof(i_0_2215,plain,
! [X4088,X4089,X4090] :
( ~ class_Orderings_Olinorder(X4090)
| c_Orderings_Oord__class_Oless__eq(X4090,X4089,X4088)
| c_Orderings_Oord__class_Oless(X4090,X4088,X4089) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_2216,plain,
! [X4073,X4074,X4075] :
( ~ class_Orderings_Olinorder(X4075)
| c_Orderings_Oord__class_Oless__eq(X4075,X4074,X4073)
| c_Orderings_Oord__class_Oless(X4075,X4073,X4074) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1375])]) ).
fof(i_0_2217,plain,
! [X4076,X4077,X4078] :
( ~ class_Orderings_Olinorder(X4078)
| c_Orderings_Oord__class_Oless(X4078,X4077,X4076)
| c_Orderings_Oord__class_Oless__eq(X4078,X4076,X4077) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1376])]) ).
fof(i_0_2218,plain,
! [X3074,X3075,X3076] :
( ~ class_Orderings_Olinorder(X3076)
| c_Orderings_Oord__class_Oless__eq(X3076,X3075,X3074)
| c_Orderings_Oord__class_Oless__eq(X3076,X3074,X3075) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_2219,plain,
! [X3022,X3023,X3024] :
( ~ class_Orderings_Olinorder(X3024)
| c_Orderings_Oord__class_Oless__eq(X3024,X3023,X3022)
| c_Orderings_Oord__class_Oless__eq(X3024,X3022,X3023) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1377])]) ).
fof(i_0_2220,plain,
! [X3185,X3186,X3187] :
( ~ class_Rings_Ocomm__semiring__1(X3187)
| c_Groups_Oplus__class_Oplus(X3187,X3186,X3185) = c_Groups_Oplus__class_Oplus(X3187,X3185,X3186) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_2221,plain,
! [X4753,X4754,X4755] :
( ~ class_Groups_Ogroup__add(X4755)
| c_Groups_Oplus__class_Oplus(X4755,X4754,X4753) != c_Groups_Ozero__class_Ozero(X4755)
| c_Groups_Ouminus__class_Ouminus(X4755,X4754) = X4753 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).
fof(i_0_2222,plain,
! [X4763,X4764,X4765] :
( ( X4764 != c_Groups_Ouminus__class_Ouminus(X4765,X4763)
| c_Groups_Oplus__class_Oplus(X4765,X4764,X4763) = c_Groups_Ozero__class_Ozero(X4765)
| ~ class_Groups_Ogroup__add(X4765) )
& ( c_Groups_Oplus__class_Oplus(X4765,X4764,X4763) != c_Groups_Ozero__class_Ozero(X4765)
| X4764 = c_Groups_Ouminus__class_Ouminus(X4765,X4763)
| ~ class_Groups_Ogroup__add(X4765) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).
fof(i_0_2223,plain,
! [X4756,X4757,X4758] :
( ( c_Groups_Oplus__class_Oplus(X4758,X4757,X4756) != c_Groups_Ozero__class_Ozero(X4758)
| X4756 = c_Groups_Ouminus__class_Ouminus(X4758,X4757)
| ~ class_Groups_Ogroup__add(X4758) )
& ( X4756 != c_Groups_Ouminus__class_Ouminus(X4758,X4757)
| c_Groups_Oplus__class_Oplus(X4758,X4757,X4756) = c_Groups_Ozero__class_Ozero(X4758)
| ~ class_Groups_Ogroup__add(X4758) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff])])]) ).
fof(i_0_2224,plain,
! [X3639,X3640,X3641] :
( ( c_Polynomial_Omonom(X3641,X3640,X3639) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3641))
| X3640 = c_Groups_Ozero__class_Ozero(X3641)
| ~ class_Groups_Ozero(X3641) )
& ( X3640 != c_Groups_Ozero__class_Ozero(X3641)
| c_Polynomial_Omonom(X3641,X3640,X3639) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3641))
| ~ class_Groups_Ozero(X3641) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__0__iff])])]) ).
fof(i_0_2225,plain,
! [X3941] :
( ~ class_Rings_Olinordered__semidom(X3941)
| ~ c_Orderings_Oord__class_Oless(X3941,c_Groups_Oone__class_Oone(X3941),c_Groups_Ozero__class_Ozero(X3941)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1378])]) ).
fof(i_0_2226,plain,
! [X4304] :
( ~ class_Rings_Olinordered__semidom(X4304)
| ~ c_Orderings_Oord__class_Oless__eq(X4304,c_Groups_Oone__class_Oone(X4304),c_Groups_Ozero__class_Ozero(X4304)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1379])]) ).
fof(i_0_2227,plain,
! [X3593,X3594] :
( ~ class_Rings_Ocomm__semiring__0(X3594)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3594)),X3593),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3594))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3594)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__right])]) ).
cnf(i_0_2228,plain,
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_1380]) ).
fof(i_0_2229,plain,
! [X3383,X3384,X3385] :
( ~ class_Rings_Ocomm__semiring__1(X3385)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3385),X3384),X3383) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3385),X3383),X3384) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
cnf(i_0_2230,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = 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_1340]) ).
fof(i_0_2231,plain,
! [X5132,X5133] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5133,X5132)
| X5133 = X5132
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5132,X5133) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_2232,plain,
! [X4025,X4026] :
( ( X4026 = X4025
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4026,X4025)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4025,X4026) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4026,X4025)
| X4026 != X4025 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4025,X4026)
| X4026 != X4025 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_2233,plain,
! [X4023,X4024] :
( X4024 = X4023
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4024,X4023)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4023,X4024) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1381])]) ).
fof(i_0_2234,plain,
! [X5292,X5293] :
( ~ class_Rings_Ocomm__semiring__1(X5293)
| ~ c_Rings_Odvd__class_Odvd(X5293,c_Groups_Ozero__class_Ozero(X5293),X5292)
| X5292 = c_Groups_Ozero__class_Ozero(X5293) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__left])]) ).
fof(i_0_2235,plain,
! [X5166,X5167] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5167,X5166)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5166,X5167) ),
inference(variable_rename,[status(thm)],[fact_zle__linear]) ).
fof(i_0_2236,plain,
! [X3255,X3256] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3256,X3255)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3255,X3256) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_2237,plain,
! [X3114,X3115] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3115,X3114)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3114,X3115) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(i_0_2238,plain,
! [X3764,X3765,X3766] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3766),X3765),X3764) != c_Groups_Ozero__class_Ozero(X3766)
| X3765 = c_Groups_Ozero__class_Ozero(X3766)
| X3764 = c_Groups_Ozero__class_Ozero(X3766)
| ~ class_Rings_Oring__no__zero__divisors(X3766) )
& ( X3765 != c_Groups_Ozero__class_Ozero(X3766)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3766),X3765),X3764) = c_Groups_Ozero__class_Ozero(X3766)
| ~ class_Rings_Oring__no__zero__divisors(X3766) )
& ( X3764 != c_Groups_Ozero__class_Ozero(X3766)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3766),X3765),X3764) = c_Groups_Ozero__class_Ozero(X3766)
| ~ class_Rings_Oring__no__zero__divisors(X3766) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_2239,plain,
! [X3761,X3762,X3763] :
( ~ class_Rings_Ono__zero__divisors(X3763)
| X3762 = c_Groups_Ozero__class_Ozero(X3763)
| X3761 = c_Groups_Ozero__class_Ozero(X3763)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3763),X3762),X3761) != c_Groups_Ozero__class_Ozero(X3763) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_2240,plain,
! [X3758,X3759,X3760] :
( ~ class_Rings_Ono__zero__divisors(X3760)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3760),X3759),X3758) != c_Groups_Ozero__class_Ozero(X3760)
| X3759 = c_Groups_Ozero__class_Ozero(X3760)
| X3758 = c_Groups_Ozero__class_Ozero(X3760) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_2241,plain,
! [X4881,X4882] :
( ~ class_Groups_Oab__group__add(X4882)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4882),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4882)),X4881) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4882),X4881) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J])]) ).
fof(i_0_2242,plain,
! [X5150,X5151] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5151,X5150) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5150,X5151),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_2243,plain,
! [X3700,X3701] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3701,X3700) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3700,X3701),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_2244,plain,
! [X3136,X3137] :
( ( c_Groups_Oplus__class_Oplus(X3137,X3136,X3136) != c_Groups_Ozero__class_Ozero(X3137)
| X3136 = c_Groups_Ozero__class_Ozero(X3137)
| ~ class_Groups_Olinordered__ab__group__add(X3137) )
& ( X3136 != c_Groups_Ozero__class_Ozero(X3137)
| c_Groups_Oplus__class_Oplus(X3137,X3136,X3136) = c_Groups_Ozero__class_Ozero(X3137)
| ~ class_Groups_Olinordered__ab__group__add(X3137) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_2245,plain,
! [X2991,X2992] :
( ( c_Groups_Ozero__class_Ozero(X2992) != c_Groups_Oplus__class_Oplus(X2992,X2991,X2991)
| X2991 = c_Groups_Ozero__class_Ozero(X2992)
| ~ class_Groups_Olinordered__ab__group__add(X2992) )
& ( X2991 != c_Groups_Ozero__class_Ozero(X2992)
| c_Groups_Ozero__class_Ozero(X2992) = c_Groups_Oplus__class_Oplus(X2992,X2991,X2991)
| ~ class_Groups_Olinordered__ab__group__add(X2992) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_2246,plain,
! [X3511,X3512,X3513] :
( ( c_Groups_Ominus__class_Ominus(X3513,X3512,X3511) != c_Groups_Ozero__class_Ozero(X3513)
| X3512 = X3511
| ~ class_Groups_Ogroup__add(X3513) )
& ( X3512 != X3511
| c_Groups_Ominus__class_Ominus(X3513,X3512,X3511) = c_Groups_Ozero__class_Ozero(X3513)
| ~ class_Groups_Ogroup__add(X3513) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
fof(i_0_2247,plain,
! [X3508,X3509,X3510] :
( ( X3509 != X3508
| c_Groups_Ominus__class_Ominus(X3510,X3509,X3508) = c_Groups_Ozero__class_Ozero(X3510)
| ~ class_Groups_Oab__group__add(X3510) )
& ( c_Groups_Ominus__class_Ominus(X3510,X3509,X3508) != c_Groups_Ozero__class_Ozero(X3510)
| X3509 = X3508
| ~ class_Groups_Oab__group__add(X3510) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).
fof(i_0_2248,plain,
! [X4977,X4978,X4979] :
( ~ class_Rings_Oring__1__no__zero__divisors(X4979)
| X4978 = c_Groups_Ozero__class_Ozero(X4979)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4979),X4978),X4977) != c_Groups_Ozero__class_Ozero(X4979) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_2249,plain,
! [X4812,X4813] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4813,X4812) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X4812 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4813) )
& ( X4812 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4813)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4813,X4812) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__eq__0__iff])]) ).
fof(i_0_2250,plain,
! [X3138,X3139,X3140] :
( ( X3139 != c_Groups_Oplus__class_Oplus(X3140,X3139,X3138)
| X3138 = c_Groups_Ozero__class_Ozero(X3140)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3140) )
& ( X3138 != c_Groups_Ozero__class_Ozero(X3140)
| X3139 = c_Groups_Oplus__class_Oplus(X3140,X3139,X3138)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_2251,plain,
! [X2999,X3000] :
( ( c_Polynomial_Opoly(X3000,X2999) != c_Polynomial_Opoly(X3000,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3000)))
| X2999 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3000))
| ~ class_Int_Oring__char__0(X3000)
| ~ class_Rings_Oidom(X3000) )
& ( X2999 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3000))
| c_Polynomial_Opoly(X3000,X2999) = c_Polynomial_Opoly(X3000,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3000)))
| ~ class_Int_Oring__char__0(X3000)
| ~ class_Rings_Oidom(X3000) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__zero])])]) ).
fof(i_0_2252,plain,
! [X3992,X3993,X3994] :
( ~ class_Orderings_Oorder(X3994)
| ~ c_Orderings_Oord__class_Oless(X3994,X3993,X3992)
| X3993 != X3992 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_2253,plain,
! [X3983,X3984,X3985] :
( ~ class_Orderings_Oorder(X3985)
| ~ c_Orderings_Oord__class_Oless(X3985,X3984,X3983)
| X3984 != X3983 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_2254,plain,
! [X3980,X3981,X3982] :
( ~ class_Orderings_Oorder(X3982)
| ~ c_Orderings_Oord__class_Oless(X3982,X3981,X3980)
| X3980 != X3981 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_2255,plain,
! [X2973] :
( ~ class_Groups_Ozero(X2973)
| c_Polynomial_OpCons(X2973,c_Groups_Ozero__class_Ozero(X2973),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2973))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2973)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__0__0])]) ).
fof(i_0_2256,plain,
! [X4029] :
( ~ class_Rings_Ocomm__semiring__1(X4029)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4029)) = c_Polynomial_OpCons(X4029,c_Groups_Oone__class_Oone(X4029),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4029))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__poly__def])]) ).
fof(i_0_2257,plain,
! [X5221] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5221,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatceiling(X5221) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__neg])]) ).
fof(i_0_2258,plain,
! [X4883] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4883,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(X4883) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__neg])]) ).
fof(i_0_2259,plain,
! [X4149] :
( ( X4149 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4149) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4149)
| X4149 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_2260,plain,
! [X4012,X4013] :
( ~ class_Orderings_Opreorder(X4013)
| ~ c_Orderings_Oord__class_Oless(X4013,X4012,X4012) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1382])]) ).
fof(i_0_2261,plain,
! [X5373] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5373,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X5373 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X5373 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5373,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1])]) ).
fof(i_0_2262,plain,
! [X3656] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3656,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3656 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3656,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])]) ).
cnf(i_0_2263,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1383]) ).
cnf(i_0_2264,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1384]) ).
cnf(i_0_2265,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1385]) ).
cnf(i_0_2266,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1386]) ).
cnf(i_0_2267,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1387]) ).
cnf(i_0_2268,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1388]) ).
fof(i_0_2269,plain,
! [X4975,X4976] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4976),X4975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4975),X4976),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_2270,plain,
! [X3733,X3734] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3734),X3733) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3733),X3734),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_2271,plain,
! [X3750,X3751] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3751),X3750) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3750),X3751),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(i_0_2272,plain,
! [X4761,X4762] :
( ~ class_Groups_Ogroup__add(X4762)
| c_Groups_Oplus__class_Oplus(X4762,c_Groups_Ouminus__class_Ouminus(X4762,X4761),X4761) = c_Groups_Ozero__class_Ozero(X4762) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).
fof(i_0_2273,plain,
! [X4759,X4760] :
( ~ class_Groups_Oab__group__add(X4760)
| c_Groups_Oplus__class_Oplus(X4760,c_Groups_Ouminus__class_Ouminus(X4760,X4759),X4759) = c_Groups_Ozero__class_Ozero(X4760) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).
fof(i_0_2274,plain,
! [X4766,X4767] :
( ~ class_Groups_Ogroup__add(X4767)
| c_Groups_Oplus__class_Oplus(X4767,X4766,c_Groups_Ouminus__class_Ouminus(X4767,X4766)) = c_Groups_Ozero__class_Ozero(X4767) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).
fof(i_0_2275,plain,
! [X3654,X3655] :
( ( X3655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3655,X3654) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3655,X3654) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3655 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3654 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3655,X3654) = 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_2276,plain,
! [X3871,X3872] :
( ~ class_Rings_Ocomm__semiring__0(X3872)
| c_Polynomial_Opcompose(X3872,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3872)),X3871) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3872)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__0])]) ).
fof(i_0_2277,plain,
! [X3176,X3177] :
( ~ class_Rings_Ocomm__semiring__0(X3177)
| c_Polynomial_Osynthetic__div(X3177,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3177)),X3176) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__0])]) ).
fof(i_0_2278,plain,
! [X3183,X3184] :
( ~ class_Rings_Ocomm__semiring__0(X3184)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3184,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3184)),X3183) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__0])]) ).
fof(i_0_2279,plain,
! [X3586,X3587] :
( ~ class_Rings_Ocomm__semiring__0(X3587)
| c_Polynomial_Osmult(X3587,X3586,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3587))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3587)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__right])]) ).
fof(i_0_2280,plain,
! [X4146,X4147] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4147,X4146)
| X4146 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr__implies__not0])]) ).
cnf(i_0_2281,plain,
c_Nat_OSuc(X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1389]) ).
cnf(i_0_2282,plain,
X1 != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1390]) ).
fof(i_0_2283,plain,
! [X3178,X3179] :
( ~ class_RealVector_Oreal__normed__vector(X3179)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3179,X3178)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).
fof(i_0_2284,plain,
! [X5057,X5058] :
( ( X5057 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5058),c_Groups_Ozero__class_Ozero(X5058)),X5057) = c_Groups_Oone__class_Oone(X5058)
| ~ class_Power_Opower(X5058)
| ~ class_Rings_Osemiring__0(X5058) )
& ( X5057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5058),c_Groups_Ozero__class_Ozero(X5058)),X5057) = c_Groups_Ozero__class_Ozero(X5058)
| ~ class_Power_Opower(X5058)
| ~ class_Rings_Osemiring__0(X5058) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_2285,plain,
! [X3652,X3653] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3653,X3652) != X3653
| X3652 = 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_2286,plain,
! [X4150] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4150,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1391]) ).
fof(i_0_2287,plain,
! [X4148] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4148,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1392]) ).
fof(i_0_2288,plain,
! [X3931] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3931,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1393]) ).
fof(i_0_2289,plain,
! [X5547] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5547,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X5547))),
inference(variable_rename,[status(thm)],[fact_real__natceiling__ge]) ).
fof(i_0_2290,plain,
! [X3942,X3943] :
( ~ class_Rings_Ocomm__semiring__1(X3943)
| hAPP(c_Polynomial_Opoly(X3943,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X3943))),X3942) = c_Groups_Oone__class_Oone(X3943) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__1])]) ).
fof(i_0_2291,plain,
! [X2974,X2975] :
( ~ class_Rings_Ocomm__semiring__0(X2975)
| hAPP(c_Polynomial_Opoly(X2975,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2975))),X2974) = c_Groups_Ozero__class_Ozero(X2975) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
fof(i_0_2292,plain,
! [X4020,X4021] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4021,X4020)
| X4020 != X4021 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_2293,plain,
! [X4018,X4019] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4019,X4018)
| X4019 != X4018 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_2294,plain,
! [X2976,X2977] :
( ~ class_Groups_Ocomm__monoid__add(X2977)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2977),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2977)),X2976) = X2976 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])]) ).
fof(i_0_2295,plain,
! [X3578,X3579] :
( ~ class_Groups_Oab__group__add(X3579)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3579),X3578,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3579))) = X3578 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J])]) ).
fof(i_0_2296,plain,
! [X2980,X2981] :
( ~ class_Groups_Ocomm__monoid__add(X2981)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2981),X2980,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2981))) = X2980 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])]) ).
fof(i_0_2297,plain,
! [X4538,X4539] :
( ~ class_Rings_Olinordered__idom(X4539)
| X4538 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4539))
| c_Polynomial_Opos__poly(X4539,X4538)
| c_Polynomial_Opos__poly(X4539,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4539),X4538)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__total])]) ).
fof(i_0_2298,plain,
! [X3494,X3495] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3495),X3494) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3495 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3495 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3495),X3494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3494 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3495),X3494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__is__0])])]) ).
fof(i_0_2299,plain,
! [X4027] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4027,X4027),
inference(variable_rename,[status(thm)],[i_0_1394]) ).
fof(i_0_2300,plain,
! [X4022] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4022,X4022),
inference(variable_rename,[status(thm)],[i_0_1395]) ).
fof(i_0_2301,plain,
! [X4351,X4352] :
( X4352 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4352),X4351)
| X4351 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4352 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10])]) ).
fof(i_0_2302,plain,
! [X4768,X4769] :
( ~ class_Groups_Ogroup__add(X4769)
| c_Groups_Ominus__class_Ominus(X4769,c_Groups_Ozero__class_Ozero(X4769),X4768) = c_Groups_Ouminus__class_Ouminus(X4769,X4768) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).
fof(i_0_2303,plain,
! [X4202,X4203] :
( ( X4203 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4203),X4202) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4202 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4203),X4202) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4203 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4202 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4203),X4202) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff])])]) ).
fof(i_0_2304,plain,
! [X4205,X4206] :
( ( X4206 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4206),X4205) )
& ( X4205 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4206),X4205) )
& ( X4206 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4205 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4206),X4205) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).
fof(i_0_2305,plain,
! [X5531] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5531)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__ge__zero]) ).
fof(i_0_2306,plain,
! [X5140] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5140),X5140) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(i_0_2307,plain,
! [X3637,X3638] :
( ~ class_Groups_Ozero(X3638)
| c_Polynomial_Omonom(X3638,c_Groups_Ozero__class_Ozero(X3638),X3637) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3638)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__0])]) ).
fof(i_0_2308,plain,
! [X3622,X3623] :
( ~ class_Rings_Ocomm__semiring__0(X3623)
| c_Polynomial_Osmult(X3623,c_Groups_Ozero__class_Ozero(X3623),X3622) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3623)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__left])]) ).
fof(i_0_2309,plain,
! [X5208] :
( ~ class_Power_Opower(X5208)
| c_Power_Opower__class_Opower(X5208) = c_Power_Opower_Opower(X5208,c_Groups_Oone__class_Oone(X5208),c_Groups_Otimes__class_Otimes(X5208)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).
fof(i_0_2310,plain,
! [X4987,X4988] :
( ~ class_Groups_Omonoid__mult(X4988)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4988),c_Groups_Oone__class_Oone(X4988)),X4987) = c_Groups_Oone__class_Oone(X4988) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_2311,plain,
! [X3769,X3770] :
( ~ class_Rings_Omult__zero(X3770)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3770),c_Groups_Ozero__class_Ozero(X3770)),X3769) = c_Groups_Ozero__class_Ozero(X3770) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_2312,plain,
! [X3527,X3528] :
( ~ class_RealVector_Oreal__normed__algebra(X3528)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3528),c_Groups_Ozero__class_Ozero(X3528)),X3527) = c_Groups_Ozero__class_Ozero(X3528) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).
fof(i_0_2313,plain,
! [X3525,X3526] :
( ~ class_RealVector_Oreal__normed__algebra(X3526)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3526),c_Groups_Ozero__class_Ozero(X3526)),X3525) = c_Groups_Ozero__class_Ozero(X3526) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).
fof(i_0_2314,plain,
! [X3533,X3534] :
( ~ class_Rings_Ocomm__semiring__1(X3534)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3534),c_Groups_Ozero__class_Ozero(X3534)),X3533) = c_Groups_Ozero__class_Ozero(X3534) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(i_0_2315,plain,
! [X3940] :
( ~ class_Rings_Olinordered__semidom(X3940)
| c_Orderings_Oord__class_Oless(X3940,c_Groups_Ozero__class_Ozero(X3940),c_Groups_Oone__class_Oone(X3940)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_2316,plain,
! [X4305] :
( ~ class_Rings_Olinordered__semidom(X4305)
| c_Orderings_Oord__class_Oless__eq(X4305,c_Groups_Ozero__class_Ozero(X4305),c_Groups_Oone__class_Oone(X4305)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_2317,plain,
! [X4143,X4144] :
( ~ class_Groups_Omonoid__mult(X4144)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4144),c_Groups_Oone__class_Oone(X4144)),X4143) = X4143 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_2318,plain,
! [X4141,X4142] :
( ~ class_Groups_Ocomm__monoid__mult(X4142)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4142),c_Groups_Oone__class_Oone(X4142)),X4141) = X4141 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_2319,plain,
! [X4135,X4136] :
( ~ class_Rings_Ocomm__semiring__1(X4136)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4136),c_Groups_Oone__class_Oone(X4136)),X4135) = X4135 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
fof(i_0_2320,plain,
! [X3767,X3768] :
( ~ class_Rings_Omult__zero(X3768)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3768),X3767),c_Groups_Ozero__class_Ozero(X3768)) = c_Groups_Ozero__class_Ozero(X3768) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_2321,plain,
! [X3531,X3532] :
( ~ class_RealVector_Oreal__normed__algebra(X3532)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3532),X3531),c_Groups_Ozero__class_Ozero(X3532)) = c_Groups_Ozero__class_Ozero(X3532) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).
fof(i_0_2322,plain,
! [X3529,X3530] :
( ~ class_RealVector_Oreal__normed__algebra(X3530)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3530),X3529),c_Groups_Ozero__class_Ozero(X3530)) = c_Groups_Ozero__class_Ozero(X3530) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
fof(i_0_2323,plain,
! [X3535,X3536] :
( ~ class_Rings_Ocomm__semiring__1(X3536)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3536),X3535),c_Groups_Ozero__class_Ozero(X3536)) = c_Groups_Ozero__class_Ozero(X3536) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(i_0_2324,plain,
! [X4208,X4209] :
( ~ class_Rings_Ocomm__semiring__1(X4209)
| c_Polynomial_Osmult(X4209,c_Groups_Oone__class_Oone(X4209),X4208) = X4208 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__1__left])]) ).
fof(i_0_2325,plain,
! [X3143,X3144] :
( ~ class_Rings_Ocomm__semiring__1(X3144)
| c_Groups_Oplus__class_Oplus(X3144,c_Groups_Ozero__class_Ozero(X3144),X3143) = X3143 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_2326,plain,
! [X2995,X2996] :
( ~ class_Groups_Omonoid__add(X2996)
| c_Groups_Oplus__class_Oplus(X2996,c_Groups_Ozero__class_Ozero(X2996),X2995) = X2995 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_2327,plain,
! [X2993,X2994] :
( ~ class_Groups_Ocomm__monoid__add(X2994)
| c_Groups_Oplus__class_Oplus(X2994,c_Groups_Ozero__class_Ozero(X2994),X2993) = X2993 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_2328,plain,
! [X3504,X3505] :
( ~ class_Groups_Ogroup__add(X3505)
| c_Groups_Ominus__class_Ominus(X3505,X3504,c_Groups_Ozero__class_Ozero(X3505)) = X3504 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).
fof(i_0_2329,plain,
! [X3141,X3142] :
( ~ class_Rings_Ocomm__semiring__1(X3142)
| c_Groups_Oplus__class_Oplus(X3142,X3141,c_Groups_Ozero__class_Ozero(X3142)) = X3141 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_2330,plain,
! [X2989,X2990] :
( ~ class_Groups_Omonoid__add(X2990)
| c_Groups_Oplus__class_Oplus(X2990,X2989,c_Groups_Ozero__class_Ozero(X2990)) = X2989 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_2331,plain,
! [X2987,X2988] :
( ~ class_Groups_Ocomm__monoid__add(X2988)
| c_Groups_Oplus__class_Oplus(X2988,X2987,c_Groups_Ozero__class_Ozero(X2988)) = X2987 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_2332,plain,
! [X5298,X5299] :
( ~ class_Rings_Ocomm__semiring__1(X5299)
| c_Rings_Odvd__class_Odvd(X5299,c_Groups_Oone__class_Oone(X5299),X5298) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__dvd])]) ).
fof(i_0_2333,plain,
! [X5227,X5228] :
( ~ class_Rings_Ocomm__semiring__1(X5228)
| c_Rings_Odvd__class_Odvd(X5228,X5227,c_Groups_Ozero__class_Ozero(X5228)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])]) ).
fof(i_0_2334,plain,
! [X5031,X5032] :
( ~ class_Power_Opower(X5032)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5032),X5031),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5032) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_2335,plain,
! [X4786,X4787] :
( ~ class_Rings_Ocomm__semiring__1(X4787)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4787),X4786),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4787) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
fof(i_0_2336,plain,
! [X4139,X4140] :
( ~ class_Groups_Omonoid__mult(X4140)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4140),X4139),c_Groups_Oone__class_Oone(X4140)) = X4139 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_2337,plain,
! [X4137,X4138] :
( ~ class_Groups_Ocomm__monoid__mult(X4138)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4138),X4137),c_Groups_Oone__class_Oone(X4138)) = X4137 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_2338,plain,
! [X4133,X4134] :
( ~ class_Rings_Ocomm__semiring__1(X4134)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4134),X4133),c_Groups_Oone__class_Oone(X4134)) = X4133 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(i_0_2339,plain,
! [X3506,X3507] :
( ~ class_Groups_Ogroup__add(X3507)
| c_Groups_Ominus__class_Ominus(X3507,X3506,X3506) = c_Groups_Ozero__class_Ozero(X3507) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(i_0_2340,plain,
! [X3068,X3069,X3070] :
( ~ class_Orderings_Opreorder(X3070)
| X3069 != X3068
| c_Orderings_Oord__class_Oless__eq(X3070,X3069,X3068) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_2341,plain,
! [X5001,X5002] :
( ~ class_Groups_Omonoid__mult(X5002)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5002),X5001),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X5001 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_2342,plain,
! [X4664,X4665] :
( ~ class_Rings_Ocomm__semiring__1(X4665)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4665),X4664),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4664 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).
fof(i_0_2343,plain,
! [X5209] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X5209)),
inference(variable_rename,[status(thm)],[fact_zero__le__natceiling]) ).
fof(i_0_2344,plain,
! [X4731] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X4731)),
inference(variable_rename,[status(thm)],[fact_zero__le__natfloor]) ).
fof(i_0_2345,plain,
! [X5278,X5279] :
( ~ class_Rings_Ocomm__semiring__1(X5279)
| c_Rings_Odvd__class_Odvd(X5279,X5278,X5278) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__refl])]) ).
fof(i_0_2346,plain,
! [X2937,X2938] :
( ~ class_Orderings_Opreorder(X2938)
| c_Orderings_Oord__class_Oless__eq(X2938,X2937,X2937) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
cnf(i_0_2347,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]) ).
fof(i_0_2348,plain,
! [X4649,X4650] :
( ~ class_RealVector_Oreal__normed__vector(X4650)
| c_RealVector_Onorm__class_Onorm(X4650,c_Groups_Ouminus__class_Ouminus(X4650,X4649)) = c_RealVector_Onorm__class_Onorm(X4650,X4649) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel])]) ).
fof(i_0_2349,plain,
! [X3122,X3123,X3124] :
( ( c_Polynomial_Opoly(X3124,X3123) != c_Polynomial_Opoly(X3124,X3122)
| X3123 = X3122
| ~ class_Int_Oring__char__0(X3124)
| ~ class_Rings_Oidom(X3124) )
& ( X3123 != X3122
| c_Polynomial_Opoly(X3124,X3123) = c_Polynomial_Opoly(X3124,X3122)
| ~ class_Int_Oring__char__0(X3124)
| ~ class_Rings_Oidom(X3124) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])]) ).
fof(i_0_2350,plain,
! [X4145] :
( X4145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4145) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_2351,plain,
! [X4794] :
( ~ class_Rings_Olinordered__idom(X4794)
| ~ c_Polynomial_Opos__poly(X4794,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4794))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1396])]) ).
fof(i_0_2352,plain,
! [X3483] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3483) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).
fof(i_0_2353,plain,
! [X5148] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5148) = X5148,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_2354,plain,
! [X3658] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3658) = X3658,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_2355,plain,
! [X3482] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3482,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3482,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(i_0_2356,plain,
! [X5149] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5149,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X5149,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_2357,plain,
! [X3657] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3657,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3657,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_2358,plain,
! [X5445,X5446] :
( X5446 != X5445
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5446,X5445) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl])]) ).
fof(i_0_2359,plain,
! [X3271,X3272] :
( X3272 != X3271
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3272,X3271) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_2360,plain,
! [X5498] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5498),
inference(variable_rename,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Obot__least]) ).
fof(i_0_2361,plain,
! [X3239] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3239),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_2362,plain,
! [X3211] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3211),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_2363,plain,
! [X5497] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5497,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Otop__greatest]) ).
fof(i_0_2364,plain,
! [X4711] :
( ~ class_Groups_Oab__group__add(X4711)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4711),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4711))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4711)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J])]) ).
fof(i_0_2365,plain,
! [X3481] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3481,X3481) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).
fof(i_0_2366,plain,
! [X3497] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3497) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_2367,plain,
! [X4529,X4530,X4531] :
( ( c_Groups_Ouminus__class_Ouminus(X4531,X4530) != c_Groups_Ouminus__class_Ouminus(X4531,X4529)
| X4530 = X4529
| ~ class_Groups_Ogroup__add(X4531) )
& ( X4530 != X4529
| c_Groups_Ouminus__class_Ouminus(X4531,X4530) = c_Groups_Ouminus__class_Ouminus(X4531,X4529)
| ~ class_Groups_Ogroup__add(X4531) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).
fof(i_0_2368,plain,
! [X4957] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X4957) = X4957,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_2369,plain,
! [X4207] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4207) = X4207,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_2370,plain,
! [X4721] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X4721) = X4721,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(i_0_2371,plain,
! [X5436] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5436,X5436),
inference(variable_rename,[status(thm)],[fact_dvd_Oorder__refl]) ).
fof(i_0_2372,plain,
! [X5165] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5165,X5165),
inference(variable_rename,[status(thm)],[fact_zle__refl]) ).
fof(i_0_2373,plain,
! [X3240] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3240,X3240),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_2374,plain,
! [X3116] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3116,X3116),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(i_0_2375,plain,
! [X3496] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3496),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0__right]) ).
fof(i_0_2376,plain,
! [X4956] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4956),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X4956,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_2377,plain,
! [X4204] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4204),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4204,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_2378,plain,
! [X5791,X5792] :
( ~ hBOOL(c_fequal(X5792,X5791))
| X5792 = X5791 ),
inference(variable_rename,[status(thm)],[i_0_1397]) ).
fof(i_0_2379,plain,
! [X4521,X4522] :
( ~ class_Groups_Ogroup__add(X4522)
| c_Groups_Ouminus__class_Ouminus(X4522,c_Groups_Ouminus__class_Ouminus(X4522,X4521)) = X4521 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
fof(i_0_2380,plain,
! [X4526,X4527,X4528] :
( ( c_Groups_Ouminus__class_Ouminus(X4528,X4527) != X4526
| c_Groups_Ouminus__class_Ouminus(X4528,X4526) = X4527
| ~ class_Groups_Ogroup__add(X4528) )
& ( c_Groups_Ouminus__class_Ouminus(X4528,X4526) != X4527
| c_Groups_Ouminus__class_Ouminus(X4528,X4527) = X4526
| ~ class_Groups_Ogroup__add(X4528) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).
fof(i_0_2381,plain,
! [X4523,X4524,X4525] :
( ( X4524 != c_Groups_Ouminus__class_Ouminus(X4525,X4523)
| X4523 = c_Groups_Ouminus__class_Ouminus(X4525,X4524)
| ~ class_Groups_Ogroup__add(X4525) )
& ( X4523 != c_Groups_Ouminus__class_Ouminus(X4525,X4524)
| X4524 = c_Groups_Ouminus__class_Ouminus(X4525,X4523)
| ~ class_Groups_Ogroup__add(X4525) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).
fof(i_0_2382,plain,
! [X3209,X3210] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3210,X3209) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3209 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3210))
| ~ class_Groups_Ozero(X3210) )
& ( X3209 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3210))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3210,X3209) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X3210) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff])])]) ).
fof(i_0_2383,plain,
! [X5543,X5544] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X5544) != c_RealDef_Oreal(tc_Nat_Onat,X5543)
| X5544 = X5543 )
& ( X5544 != X5543
| c_RealDef_Oreal(tc_Nat_Onat,X5544) = c_RealDef_Oreal(tc_Nat_Onat,X5543) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject])]) ).
fof(i_0_2384,plain,
! [X4572,X4573] :
( ( c_Groups_Ozero__class_Ozero(X4573) != c_Groups_Ouminus__class_Ouminus(X4573,X4572)
| c_Groups_Ozero__class_Ozero(X4573) = X4572
| ~ class_Groups_Ogroup__add(X4573) )
& ( c_Groups_Ozero__class_Ozero(X4573) != X4572
| c_Groups_Ozero__class_Ozero(X4573) = c_Groups_Ouminus__class_Ouminus(X4573,X4572)
| ~ class_Groups_Ogroup__add(X4573) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).
fof(i_0_2385,plain,
! [X4568,X4569] :
( ( c_Groups_Ouminus__class_Ouminus(X4569,X4568) != c_Groups_Ozero__class_Ozero(X4569)
| X4568 = c_Groups_Ozero__class_Ozero(X4569)
| ~ class_Groups_Ogroup__add(X4569) )
& ( X4568 != c_Groups_Ozero__class_Ozero(X4569)
| c_Groups_Ouminus__class_Ouminus(X4569,X4568) = c_Groups_Ozero__class_Ozero(X4569)
| ~ class_Groups_Ogroup__add(X4569) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).
fof(i_0_2386,plain,
! [X2982,X2983] :
( ( c_RealVector_Onorm__class_Onorm(X2983,X2982) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2982 = c_Groups_Ozero__class_Ozero(X2983)
| ~ class_RealVector_Oreal__normed__vector(X2983) )
& ( X2982 != c_Groups_Ozero__class_Ozero(X2983)
| c_RealVector_Onorm__class_Onorm(X2983,X2982) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X2983) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).
fof(i_0_2387,plain,
! [X5731,X5732] :
( ~ class_Orderings_Oorder(X5732)
| class_Orderings_Oorder(tc_fun(X5731,X5732)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_2388,plain,
! [X5733,X5734] :
( ~ class_Orderings_Oord(X5734)
| class_Orderings_Oord(tc_fun(X5733,X5734)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_2389,plain,
! [X5729,X5730] :
( ~ class_Orderings_Opreorder(X5730)
| class_Orderings_Opreorder(tc_fun(X5729,X5730)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_2390,plain,
! [X5137] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5137)) = X5137,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
fof(i_0_2391,plain,
! [X4566,X4567] :
( ( c_Groups_Ouminus__class_Ouminus(X4567,X4566) != X4566
| X4566 = c_Groups_Ozero__class_Ozero(X4567)
| ~ class_Groups_Olinordered__ab__group__add(X4567) )
& ( X4566 != c_Groups_Ozero__class_Ozero(X4567)
| c_Groups_Ouminus__class_Ouminus(X4567,X4566) = X4566
| ~ class_Groups_Olinordered__ab__group__add(X4567) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).
fof(i_0_2392,plain,
! [X4570,X4571] :
( ( X4570 != c_Groups_Ouminus__class_Ouminus(X4571,X4570)
| X4570 = c_Groups_Ozero__class_Ozero(X4571)
| ~ class_Groups_Olinordered__ab__group__add(X4571) )
& ( X4570 != c_Groups_Ozero__class_Ozero(X4571)
| X4570 = c_Groups_Ouminus__class_Ouminus(X4571,X4570)
| ~ class_Groups_Olinordered__ab__group__add(X4571) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).
fof(i_0_2393,plain,
! [X5793,X5794] :
( X5794 != X5793
| hBOOL(c_fequal(X5794,X5793)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_2394,plain,
! [X4574] :
( ~ class_Groups_Ogroup__add(X4574)
| c_Groups_Ouminus__class_Ouminus(X4574,c_Groups_Ozero__class_Ozero(X4574)) = c_Groups_Ozero__class_Ozero(X4574) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).
fof(i_0_2395,plain,
! [X4014] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4014)
| c_RealVector_Onorm__class_Onorm(X4014,c_Groups_Oone__class_Oone(X4014)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__one])]) ).
fof(i_0_2396,plain,
! [X2972] :
( ~ class_RealVector_Oreal__normed__vector(X2972)
| c_RealVector_Onorm__class_Onorm(X2972,c_Groups_Ozero__class_Ozero(X2972)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__zero])]) ).
fof(i_0_2397,plain,
! [X5548] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X5548)) = X5548,
inference(variable_rename,[status(thm)],[fact_natceiling__real__of__nat]) ).
fof(i_0_2398,plain,
! [X5542] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X5542)) = X5542,
inference(variable_rename,[status(thm)],[fact_natfloor__real__of__nat]) ).
fof(i_0_2399,plain,
! [X5551] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X5551) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X5551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5551 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X5551) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero__iff])]) ).
fof(i_0_2400,plain,
! [X4098] :
( ~ class_Rings_Ozero__neq__one(X4098)
| c_Groups_Ozero__class_Ozero(X4098) != c_Groups_Oone__class_Oone(X4098) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_2401,plain,
! [X4097] :
( ~ class_Rings_Ozero__neq__one(X4097)
| c_Groups_Oone__class_Oone(X4097) != c_Groups_Ozero__class_Ozero(X4097) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_2402,plain,
! [X5728] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5728)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X5728)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add])]) ).
fof(i_0_2403,plain,
! [X5777] :
( ~ class_Fields_Ofield(X5777)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X5777)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Oring__div])]) ).
fof(i_0_2404,plain,
! [X5765] :
( ~ class_Fields_Ofield(X5765)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X5765)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Osemiring__div])]) ).
fof(i_0_2405,plain,
! [X5790] :
( ~ class_Rings_Ocomm__semiring__1(X5790)
| class_Rings_Odvd(tc_Polynomial_Opoly(X5790)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Odvd])]) ).
fof(i_0_2406,plain,
! [X5775] :
( ~ class_Rings_Ocomm__semiring__0(X5775)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X5775)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0])]) ).
fof(i_0_2407,plain,
! [X5785] :
( ~ class_Rings_Ocomm__semiring__1(X5785)
| class_Power_Opower(tc_Polynomial_Opoly(X5785)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower])]) ).
fof(i_0_2408,plain,
! [X5745] :
( ~ class_Rings_Oidom(X5745)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X5745)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors])]) ).
fof(i_0_2409,plain,
! [X5773] :
( ~ class_Rings_Ocomm__ring__1(X5773)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X5773)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1])]) ).
fof(i_0_2410,plain,
! [X5750] :
( ~ class_Rings_Olinordered__idom(X5750)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X5750)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1])]) ).
fof(i_0_2411,plain,
! [X5784] :
( ~ class_Rings_Ocomm__ring__1(X5784)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X5784)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1])]) ).
fof(i_0_2412,plain,
! [X5753] :
( ~ class_Rings_Olinordered__idom(X5753)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X5753)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring])]) ).
fof(i_0_2413,plain,
! [X5738] :
( ~ class_Rings_Olinordered__idom(X5738)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X5738)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict])]) ).
fof(i_0_2414,plain,
! [X5740] :
( ~ class_Rings_Olinordered__idom(X5740)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X5740)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict])]) ).
fof(i_0_2415,plain,
! [X5739] :
( ~ class_Rings_Olinordered__idom(X5739)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X5739)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict])]) ).
fof(i_0_2416,plain,
! [X5772] :
( ~ class_Rings_Ocomm__semiring__1(X5772)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X5772)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult])]) ).
fof(i_0_2417,plain,
! [X5756] :
( ~ class_Rings_Ocomm__semiring__1(X5756)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X5756)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult])]) ).
fof(i_0_2418,plain,
! [X5736] :
( ~ class_Rings_Olinordered__idom(X5736)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X5736)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add])]) ).
fof(i_0_2419,plain,
! [X5768] :
( ~ class_Rings_Ocomm__semiring__1(X5768)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X5768)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one])]) ).
fof(i_0_2420,plain,
! [X5789] :
( ~ class_Rings_Ocomm__semiring__1(X5789)
| class_Groups_Oone(tc_Polynomial_Opoly(X5789)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone])]) ).
fof(i_0_2421,plain,
! [X5762] :
( ~ class_Rings_Olinordered__idom(X5762)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X5762)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom])]) ).
fof(i_0_2422,plain,
! [X5754] :
( ~ class_Rings_Olinordered__idom(X5754)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X5754)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom])]) ).
fof(i_0_2423,plain,
! [X5749] :
( ~ class_Rings_Olinordered__idom(X5749)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X5749)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring])]) ).
fof(i_0_2424,plain,
! [X5758] :
( ~ class_Rings_Olinordered__idom(X5758)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X5758)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring])]) ).
fof(i_0_2425,plain,
! [X5746] :
( ~ class_Rings_Olinordered__idom(X5746)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X5746)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring])]) ).
fof(i_0_2426,plain,
! [X5782] :
( ~ class_Rings_Ocomm__semiring__0(X5782)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X5782)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring])]) ).
fof(i_0_2427,plain,
! [X5766] :
( ~ class_Rings_Ocomm__semiring__0(X5766)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X5766)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring])]) ).
fof(i_0_2428,plain,
! [X5778] :
( ~ class_Rings_Ocomm__semiring__0(X5778)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X5778)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero])]) ).
fof(i_0_2429,plain,
! [X5748] :
( ~ class_Rings_Oidom(X5748)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X5748)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors])]) ).
fof(i_0_2430,plain,
! [X5759] :
( ~ class_Rings_Oidom(X5759)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X5759)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors])]) ).
fof(i_0_2431,plain,
! [X5761] :
( ~ class_Rings_Olinordered__idom(X5761)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X5761)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring])]) ).
fof(i_0_2432,plain,
! [X5747] :
( ~ class_Rings_Olinordered__idom(X5747)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X5747)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict])]) ).
fof(i_0_2433,plain,
! [X5769] :
( ~ class_Rings_Olinordered__idom(X5769)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X5769)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring])]) ).
fof(i_0_2434,plain,
! [X5751] :
( ~ class_Rings_Olinordered__idom(X5751)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X5751)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add])]) ).
fof(i_0_2435,plain,
! [X5776] :
( ~ class_Groups_Oab__group__add(X5776)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X5776)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add])]) ).
fof(i_0_2436,plain,
! [X5755] :
( ~ class_Rings_Ocomm__semiring__0(X5755)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X5755)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult])]) ).
fof(i_0_2437,plain,
! [X5779] :
( ~ class_Rings_Ocomm__ring(X5779)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X5779)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring])]) ).
fof(i_0_2438,plain,
! [X5767] :
( ~ class_Groups_Oab__group__add(X5767)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X5767)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add])]) ).
fof(i_0_2439,plain,
! [X5787] :
( ~ class_Rings_Ocomm__ring(X5787)
| class_Rings_Oring(tc_Polynomial_Opoly(X5787)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring])]) ).
fof(i_0_2440,plain,
! [X5763] :
( ~ class_Rings_Ocomm__semiring__1(X5763)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X5763)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])]) ).
fof(i_0_2441,plain,
! [X5735] :
( ~ class_Rings_Oidom(X5735)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X5735)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct])]) ).
fof(i_0_2442,plain,
! [X5757] :
( ~ class_Groups_Ocomm__monoid__add(X5757)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X5757)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add])]) ).
fof(i_0_2443,plain,
! [X5744] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5744)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X5744)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add])]) ).
fof(i_0_2444,plain,
! [X5752] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5752)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X5752)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add])]) ).
fof(i_0_2445,plain,
! [X5780] :
( ~ class_Rings_Olinordered__idom(X5780)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X5780)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder])]) ).
fof(i_0_2446,plain,
! [X5783] :
( ~ class_Rings_Olinordered__idom(X5783)
| class_Orderings_Oord(tc_Polynomial_Opoly(X5783)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord])]) ).
fof(i_0_2447,plain,
! [X5771] :
( ~ class_Rings_Olinordered__idom(X5771)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X5771)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder])]) ).
fof(i_0_2448,plain,
! [X5742] :
( ~ class_Rings_Olinordered__idom(X5742)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X5742)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add])]) ).
fof(i_0_2449,plain,
! [X5788] :
( ~ class_Rings_Oidom(X5788)
| class_Rings_Oidom(tc_Polynomial_Opoly(X5788)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom])]) ).
fof(i_0_2450,plain,
! [X5781] :
( ~ class_Rings_Olinordered__idom(X5781)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X5781)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0])]) ).
fof(i_0_2451,plain,
! [X5743] :
( ~ class_Rings_Olinordered__idom(X5743)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X5743)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add])]) ).
fof(i_0_2452,plain,
! [X5774] :
( ~ class_Groups_Ocomm__monoid__add(X5774)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X5774)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add])]) ).
fof(i_0_2453,plain,
! [X5786] :
( ~ class_Groups_Ozero(X5786)
| class_Groups_Ozero(tc_Polynomial_Opoly(X5786)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero])]) ).
fof(i_0_2454,plain,
! [X5741] :
( ~ class_Rings_Olinordered__idom(X5741)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X5741)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add])]) ).
fof(i_0_2455,plain,
! [X5737] :
( ~ class_Rings_Olinordered__idom(X5737)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X5737)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le])]) ).
fof(i_0_2456,plain,
! [X5760] :
( ~ class_Groups_Ocomm__monoid__add(X5760)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X5760)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add])]) ).
fof(i_0_2457,plain,
! [X5764] :
( ~ class_Rings_Ocomm__semiring__0(X5764)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X5764)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0])]) ).
fof(i_0_2458,plain,
! [X5770] :
( ~ class_Rings_Olinordered__idom(X5770)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X5770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder])]) ).
fof(i_0_2459,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).
cnf(i_0_2460,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(X2,X3),hAPP(X2,esk36_4(X2,X3,X4,X1)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X5)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_Orderings_Oord(X4) ),
inference(split_conjunct,[status(thm)],[i_0_1398]),
[final] ).
cnf(i_0_2461,plain,
( c_Polynomial_Opoly__rec(X2,X1,X3,X4,c_Polynomial_OpCons(X1,X5,X6)) = hAPP(hAPP(hAPP(X4,X5),X6),c_If(X2,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X3,c_Polynomial_Opoly__rec(X2,X1,X3,X4,X6)))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1399]),
[final] ).
cnf(i_0_2462,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(X1,X3,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2) ),
inference(rw,[status(thm)],[i_0_1400,c_0_1401]),
[final] ).
cnf(i_0_2463,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(X1,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3) ),
inference(rw,[status(thm)],[i_0_1402,c_0_1401]),
[final] ).
cnf(i_0_2464,plain,
( c_Polynomial_Opoly__rec(X4,X1,X3,X2,c_Polynomial_OpCons(X1,X5,X6)) = hAPP(hAPP(hAPP(X2,X5),X6),c_Polynomial_Opoly__rec(X4,X1,X3,X2,X6))
| ~ class_Groups_Ozero(X1)
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1403]),
[final] ).
cnf(i_0_2465,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk3_4(X3,X2,X4,X1)),hAPP(X3,esk3_4(X3,X2,X4,X1)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1404]),
[final] ).
cnf(i_0_2466,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1405]),
[final] ).
cnf(i_0_2467,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Osynthetic__div(X1,X3,X2)),c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X3),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = X3
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1406]),
[final] ).
cnf(i_0_2468,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_2469,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1408]),
[final] ).
cnf(i_0_2470,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1409]),
[final] ).
cnf(i_0_2471,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1410]),
[final] ).
cnf(i_0_2472,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1411]),
[final] ).
cnf(i_0_2473,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1412]),
[final] ).
cnf(i_0_2474,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1413]),
[final] ).
cnf(i_0_2475,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1414]),
[final] ).
cnf(i_0_2476,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Oorder(X1,X2,X3)),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_2477,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Oorder(X1,X2,X3)),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1415]),
[final] ).
cnf(i_0_2478,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_2479,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1408]),
[final] ).
cnf(i_0_2480,plain,
( c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1409]),
[final] ).
cnf(i_0_2481,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1410]),
[final] ).
cnf(i_0_2482,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1411]),
[final] ).
cnf(i_0_2483,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1412]),
[final] ).
cnf(i_0_2484,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1413]),
[final] ).
cnf(i_0_2485,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1414]),
[final] ).
cnf(i_0_2486,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk21_2(X2,X1)),X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1416]),
[final] ).
cnf(i_0_2487,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1417]),
[final] ).
cnf(i_0_2488,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3),X1),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3),X2))),X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),esk25_3(X3,X2,X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1418]),
[final] ).
cnf(i_0_2489,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),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_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),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_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1419,c_0_1401]),c_0_1401]),c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2490,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_2491,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1421]),
[final] ).
cnf(i_0_2492,hypothesis,
( v_thesis____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),esk38_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1422]),
[final] ).
cnf(i_0_2493,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1423,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2494,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1424,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2495,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk35_2(X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(rw,[status(thm)],[i_0_1425,c_0_1401]),
[final] ).
cnf(i_0_2496,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X5)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1426]),
[final] ).
cnf(i_0_2497,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X5)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1427]),
[final] ).
cnf(i_0_2498,plain,
( c_Polynomial_Opoly__rec(X4,X1,X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X3
| ~ class_Groups_Ozero(X1)
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1428]),
[final] ).
cnf(i_0_2499,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk31_2(X3,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,esk30_3(X3,X2,X1))),X1) ),
inference(rw,[status(thm)],[i_0_1429,c_0_1401]),
[final] ).
cnf(i_0_2500,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk27_2(X3,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,esk26_3(X3,X2,X1))),X1) ),
inference(rw,[status(thm)],[i_0_1430,c_0_1401]),
[final] ).
cnf(i_0_2501,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk33_2(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk32_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1431,c_0_1401]),
[final] ).
cnf(i_0_2502,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk29_2(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk28_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1432,c_0_1401]),
[final] ).
cnf(i_0_2503,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2504,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2505,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X5))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4)),X5))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1435]),
[final] ).
cnf(i_0_2506,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk22_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1436]),
[final] ).
cnf(i_0_2507,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk10_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1437]),
[final] ).
cnf(i_0_2508,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk7_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1438]),
[final] ).
cnf(i_0_2509,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_2(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk32_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1439,c_0_1401]),
[final] ).
cnf(i_0_2510,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk29_2(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk28_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1440,c_0_1401]),
[final] ).
cnf(i_0_2511,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1441]),
[final] ).
cnf(i_0_2512,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1442]),
[final] ).
cnf(i_0_2513,plain,
( X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),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_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),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_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Oidom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1443,c_0_1401]),c_0_1401]),c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2514,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1444,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2515,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4) != X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1445]),
[final] ).
cnf(i_0_2516,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1446]),
[final] ).
cnf(i_0_2517,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5) != X6
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1447]),
[final] ).
cnf(i_0_2518,plain,
( c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5),X1) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5),X6)
| X1 != c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X3,X4)),X5),X6)
| ~ class_Rings_Oring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_2519,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1449,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2520,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1450,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2521,plain,
( v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,v_cs____)),X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,esk2_2(X1,X2),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1451]),
[final] ).
cnf(i_0_2522,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1452]),
[final] ).
cnf(i_0_2523,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1453]),
[final] ).
cnf(i_0_2524,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1454]),
[final] ).
cnf(i_0_2525,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6)),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X6)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1426]),
[final] ).
cnf(i_0_2526,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6)),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X6)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1427]),
[final] ).
cnf(i_0_2527,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))),X4)
| ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rw,[status(thm)],[i_0_1455,c_0_1401]),
[final] ).
cnf(i_0_2528,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3) = X5
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1445]),
[final] ).
cnf(i_0_2529,plain,
( X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1446]),
[final] ).
cnf(i_0_2530,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4) = X6
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1447]),
[final] ).
cnf(i_0_2531,plain,
( X4 = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_2532,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3),X5)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1456]),
[final] ).
cnf(i_0_2533,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1435]),
[final] ).
cnf(i_0_2534,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,esk36_4(X3,X2,X1,X4))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(X3,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,hAPP(X3,X2))))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X5)
| ~ class_RealVector_Oreal__normed__vector(X4)
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1398]),
[final] ).
cnf(i_0_2535,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4)),X3)
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X6)
| c_Groups_Oplus__class_Oplus(X1,X5,X6) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1457]),
[final] ).
cnf(i_0_2536,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4)),X3)
| ~ class_Rings_Olinordered__semiring__1(X1)
| ~ 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,c_Groups_Ozero__class_Ozero(X1),X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X6)
| c_Groups_Oplus__class_Oplus(X1,X5,X6) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1458]),
[final] ).
cnf(i_0_2537,plain,
( hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),esk20_3(X2,X4,X1))))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(X4,X3))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1459]),
[final] ).
cnf(i_0_2538,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X2),X4),
inference(split_conjunct,[status(thm)],[i_0_1460]),
[final] ).
cnf(i_0_2539,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2540,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1462]),
[final] ).
cnf(i_0_2541,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1463]),
[final] ).
cnf(i_0_2542,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1463]),
[final] ).
cnf(i_0_2543,plain,
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1464]),
[final] ).
cnf(i_0_2544,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)),
inference(rw,[status(thm)],[i_0_1465,c_0_1401]),
[final] ).
cnf(i_0_2545,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1466]),
[final] ).
cnf(i_0_2546,plain,
( hAPP(c_Polynomial_Opoly(X1,X3),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1467]),
[final] ).
cnf(i_0_2547,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4)),c_Polynomial_OpCons(X1,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_2548,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2)
| ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1469]),
[final] ).
cnf(i_0_2549,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1470,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2550,plain,
( hAPP(c_Polynomial_Opoly(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1471]),
[final] ).
cnf(i_0_2551,plain,
( X1 = X2
| X3 = X4
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X4)) != c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
inference(split_conjunct,[status(thm)],[i_0_1472]),
[final] ).
cnf(i_0_2552,plain,
( X2 = X4
| X3 = X5
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1473]),
[final] ).
cnf(i_0_2553,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),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_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),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_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Rings_Oidom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1474,c_0_1401]),c_0_1401]),c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2554,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Divides_Odiv__class_Odiv(X1,X5,X4)) = c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1475]),
[final] ).
cnf(i_0_2555,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_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1476,c_0_1401]),c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2556,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_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1477,c_0_1401]),c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2557,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_OpCons(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1478]),
[final] ).
cnf(i_0_2558,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2559,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,esk19_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1459]),
[final] ).
cnf(i_0_2560,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1480]),
[final] ).
cnf(i_0_2561,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1481]),
[final] ).
cnf(i_0_2562,plain,
( c_Polynomial_Opcompose(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X4),c_Polynomial_Opcompose(X1,X3,X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_2563,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1483]),
[final] ).
cnf(i_0_2564,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1484]),
[final] ).
cnf(i_0_2565,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1485,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2566,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1486,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2567,plain,
( X2 = X4
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1487,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2568,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(rw,[status(thm)],[i_0_1488,c_0_1401]),
[final] ).
cnf(i_0_2569,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)),
inference(split_conjunct,[status(thm)],[i_0_1489]),
[final] ).
cnf(i_0_2570,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2))),
inference(split_conjunct,[status(thm)],[i_0_1490]),
[final] ).
cnf(i_0_2571,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1491,c_0_1401]),c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2572,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1492]),
[final] ).
cnf(i_0_2573,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk14_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1493]),
[final] ).
cnf(i_0_2574,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk13_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1494]),
[final] ).
cnf(i_0_2575,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1495,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2576,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1496,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2577,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk14_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1493]),
[final] ).
cnf(i_0_2578,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk13_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1494]),
[final] ).
cnf(i_0_2579,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X1,X2,X3)),c_Polynomial_Omonom(X1,X4,X5)) = c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X5))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1497]),
[final] ).
cnf(i_0_2580,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1498]),
[final] ).
cnf(i_0_2581,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Odiv(X1,X2,X3),c_Divides_Odiv__class_Odiv(X1,X4,X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1499]),
[final] ).
cnf(i_0_2582,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1500]),
[final] ).
cnf(i_0_2583,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X5))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_1501]),
[final] ).
cnf(i_0_2584,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1502,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2585,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1503]),
[final] ).
cnf(i_0_2586,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1504]),
[final] ).
cnf(i_0_2587,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1505]),
[final] ).
cnf(i_0_2588,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1506]),
[final] ).
cnf(i_0_2589,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2590,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ 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),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2591,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ 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),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2592,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ 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),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2593,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Oordered__semiring(X1)
| ~ 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,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2594,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Oordered__semiring(X1)
| ~ 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,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1512]),
[final] ).
cnf(i_0_2595,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X5))
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_1513]),
[final] ).
cnf(i_0_2596,plain,
( hBOOL(hAPP(X1,esk19_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4)))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Osemiring__0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1459]),
[final] ).
cnf(i_0_2597,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,c_Polynomial_Osynthetic__div(X1,X2,X3))) = c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3),c_Polynomial_Osynthetic__div(X1,X2,X3))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2598,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1515]),
[final] ).
cnf(i_0_2599,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1516]),
[final] ).
cnf(i_0_2600,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,esk35_2(X1,X2))),X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1247]),
[final] ).
cnf(i_0_2601,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),X4) = c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1517]),
[final] ).
cnf(i_0_2602,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3),esk4_2(X3,X2))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1518]),
[final] ).
cnf(i_0_2603,plain,
( c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X3,X4),X2) = c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),c_Divides_Odiv__class_Odiv(X1,X4,X2))
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1519]),
[final] ).
cnf(i_0_2604,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2)
| hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1467]),
[final] ).
cnf(i_0_2605,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),c_Groups_Ozero__class_Ozero(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1463]),
[final] ).
cnf(i_0_2606,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X3,c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X2)
| hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1471]),
[final] ).
cnf(i_0_2607,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2608,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2609,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_2610,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1521]),
[final] ).
cnf(i_0_2611,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(rw,[status(thm)],[i_0_1522,c_0_1401]),
[final] ).
cnf(i_0_2612,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Oone__class_Oone(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1523]),
[final] ).
cnf(i_0_2613,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_Oone__class_Oone(tc_Nat_Onat)),X1)
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1524,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2614,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_Oone__class_Oone(tc_Nat_Onat)),X1)
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1525,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2615,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(rw,[status(thm)],[i_0_1526,c_0_1401]),
[final] ).
cnf(i_0_2616,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_OpCons(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1527]),
[final] ).
cnf(i_0_2617,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1528]),
[final] ).
cnf(i_0_2618,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1529]),
[final] ).
cnf(i_0_2619,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2620,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2621,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1532]),
[final] ).
cnf(i_0_2622,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1533]),
[final] ).
cnf(i_0_2623,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1534]),
[final] ).
cnf(i_0_2624,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1535]),
[final] ).
cnf(i_0_2625,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1536]),
[final] ).
cnf(i_0_2626,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1537]),
[final] ).
cnf(i_0_2627,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_2628,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1539]),
[final] ).
cnf(i_0_2629,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1540]),
[final] ).
cnf(i_0_2630,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_2631,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1542]),
[final] ).
cnf(i_0_2632,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1543]),
[final] ).
cnf(i_0_2633,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5)) = c_Polynomial_OpCons(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X5))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1544]),
[final] ).
cnf(i_0_2634,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5)) = c_Polynomial_OpCons(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1545]),
[final] ).
cnf(i_0_2635,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_2636,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1547]),
[final] ).
cnf(i_0_2637,plain,
( c_Groups_Ominus__class_Ominus(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_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1548]),
[final] ).
cnf(i_0_2638,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_1549]),
[final] ).
cnf(i_0_2639,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1550]),
[final] ).
cnf(i_0_2640,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1551]),
[final] ).
cnf(i_0_2641,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X2) = c_Groups_Oplus__class_Oplus(X1,X4,c_Divides_Odiv__class_Odiv(X1,X3,X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1552]),
[final] ).
cnf(i_0_2642,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),X2) = c_Groups_Oplus__class_Oplus(X1,X4,c_Divides_Odiv__class_Odiv(X1,X3,X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1553]),
[final] ).
cnf(i_0_2643,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1554]),
[final] ).
cnf(i_0_2644,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_2645,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1556]),
[final] ).
cnf(i_0_2646,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk24_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1557]),
[final] ).
cnf(i_0_2647,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk12_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1558]),
[final] ).
cnf(i_0_2648,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk9_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1559]),
[final] ).
cnf(i_0_2649,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2650,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk23_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1561]),
[final] ).
cnf(i_0_2651,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk11_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1562]),
[final] ).
cnf(i_0_2652,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk8_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1563]),
[final] ).
cnf(i_0_2653,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Odiv(X1,X2,X4),c_Divides_Odiv__class_Odiv(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X2)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1499]),
[final] ).
cnf(i_0_2654,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1564]),
[final] ).
cnf(i_0_2655,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1565]),
[final] ).
cnf(i_0_2656,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1566]),
[final] ).
cnf(i_0_2657,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1567]),
[final] ).
cnf(i_0_2658,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1568]),
[final] ).
cnf(i_0_2659,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1569]),
[final] ).
cnf(i_0_2660,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1570]),
[final] ).
cnf(i_0_2661,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1556]),
[final] ).
cnf(i_0_2662,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_2663,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_2664,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1556]),
[final] ).
cnf(i_0_2665,plain,
( c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))
| X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1472]),
[final] ).
cnf(i_0_2666,plain,
( c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))
| X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1473]),
[final] ).
cnf(i_0_2667,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_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))
| ~ 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_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1571,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2668,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1556]),
[final] ).
cnf(i_0_2669,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_2670,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1572]),
[final] ).
cnf(i_0_2671,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1573]),
[final] ).
cnf(i_0_2672,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1574]),
[final] ).
cnf(i_0_2673,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_2674,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1576]),
[final] ).
cnf(i_0_2675,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),X4) = c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X2)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_2676,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(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(split_conjunct,[status(thm)],[i_0_1505]),
[final] ).
cnf(i_0_2677,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ 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(split_conjunct,[status(thm)],[i_0_1506]),
[final] ).
cnf(i_0_2678,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X5 = X6
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X4
| c_Groups_Oplus__class_Oplus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)) != c_Groups_Oplus__class_Oplus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_1578]),
[final] ).
cnf(i_0_2679,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1579]),
[final] ).
cnf(i_0_2680,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1580]),
[final] ).
cnf(i_0_2681,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_2682,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2683,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1583]),
[final] ).
cnf(i_0_2684,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1584]),
[final] ).
cnf(i_0_2685,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1585]),
[final] ).
cnf(i_0_2686,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_2687,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_2688,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_2689,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1589]),
[final] ).
cnf(i_0_2690,plain,
( c_RComplete_Onatceiling(X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[i_0_1590]),
[final] ).
cnf(i_0_2691,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1591]),
[final] ).
cnf(i_0_2692,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1592]),
[final] ).
cnf(i_0_2693,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1593]),
[final] ).
cnf(i_0_2694,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1594]),
[final] ).
cnf(i_0_2695,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X2,X3)),X4) = c_Polynomial_Osmult(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1595]),
[final] ).
cnf(i_0_2696,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = c_Groups_Ominus__class_Ominus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1596]),
[final] ).
cnf(i_0_2697,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1597]),
[final] ).
cnf(i_0_2698,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X5),X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1598]),
[final] ).
cnf(i_0_2699,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1493]),
[final] ).
cnf(i_0_2700,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1494]),
[final] ).
cnf(i_0_2701,plain,
( hBOOL(hAPP(X4,X3))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1493]),
[final] ).
cnf(i_0_2702,plain,
( hBOOL(hAPP(X4,X3))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1494]),
[final] ).
cnf(i_0_2703,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1599]),
[final] ).
cnf(i_0_2704,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ 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(split_conjunct,[status(thm)],[i_0_1599]),
[final] ).
cnf(i_0_2705,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_2706,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1601]),
[final] ).
cnf(i_0_2707,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1602]),
[final] ).
cnf(i_0_2708,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1603]),
[final] ).
cnf(i_0_2709,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2710,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(rw,[status(thm)],[i_0_1605,c_0_1401]),
[final] ).
cnf(i_0_2711,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1606]),
[final] ).
cnf(i_0_2712,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_1607]),
[final] ).
cnf(i_0_2713,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_1608]),
[final] ).
cnf(i_0_2714,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_1609]),
[final] ).
cnf(i_0_2715,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_1610]),
[final] ).
cnf(i_0_2716,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_1611]),
[final] ).
cnf(i_0_2717,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_1612]),
[final] ).
cnf(i_0_2718,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_1613]),
[final] ).
cnf(i_0_2719,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_1614]),
[final] ).
cnf(i_0_2720,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1615,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2721,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1616,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2722,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,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1617,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2723,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1618,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2724,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1619]),
[final] ).
cnf(i_0_2725,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X3,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1620]),
[final] ).
cnf(i_0_2726,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_2727,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1622]),
[final] ).
cnf(i_0_2728,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1500]),
[final] ).
cnf(i_0_2729,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2730,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2731,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,X3) != c_Divides_Odiv__class_Odiv(X1,X4,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,X5,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1625]),
[final] ).
cnf(i_0_2732,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2733,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X3)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2734,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[i_0_1628,c_0_1401]),
[final] ).
cnf(i_0_2735,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,X4) = c_Divides_Odiv__class_Odiv(X1,X5,X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X2)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1625]),
[final] ).
cnf(i_0_2736,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_1629]),
[final] ).
cnf(i_0_2737,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_1630]),
[final] ).
cnf(i_0_2738,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2739,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk14_3(X2,X1,X3))
| hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1493]),
[final] ).
cnf(i_0_2740,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk13_3(X2,X1,X3))
| hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1494]),
[final] ).
cnf(i_0_2741,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2742,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X4)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2743,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2744,plain,
( X2 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)
| ~ 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),X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2745,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2746,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_2747,plain,
( c_RComplete_Onatfloor(X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[i_0_1638]),
[final] ).
cnf(i_0_2748,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk14_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1493]),
[final] ).
cnf(i_0_2749,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk13_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1494]),
[final] ).
cnf(i_0_2750,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)
| ~ class_Rings_Olinordered__idom(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)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1639]),
[final] ).
cnf(i_0_2751,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2)
| ~ class_Rings_Olinordered__idom(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)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1640]),
[final] ).
cnf(i_0_2752,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_RealVector_Onorm__class_Onorm(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1641]),
[final] ).
cnf(i_0_2753,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_2754,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1642]),
[final] ).
cnf(i_0_2755,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1556]),
[final] ).
cnf(i_0_2756,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_2757,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1644]),
[final] ).
cnf(i_0_2758,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1534]),
[final] ).
cnf(i_0_2759,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1645]),
[final] ).
cnf(i_0_2760,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1646]),
[final] ).
cnf(i_0_2761,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Oordered__comm__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1647]),
[final] ).
cnf(i_0_2762,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1648]),
[final] ).
cnf(i_0_2763,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1537]),
[final] ).
cnf(i_0_2764,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_2765,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1649]),
[final] ).
cnf(i_0_2766,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1556]),
[final] ).
cnf(i_0_2767,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_2768,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_2769,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1651]),
[final] ).
cnf(i_0_2770,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1539]),
[final] ).
cnf(i_0_2771,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_2772,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_2773,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_1654]),
[final] ).
cnf(i_0_2774,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_1655]),
[final] ).
cnf(i_0_2775,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_1656]),
[final] ).
cnf(i_0_2776,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_1657]),
[final] ).
cnf(i_0_2777,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1658]),
[final] ).
cnf(i_0_2778,plain,
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_2779,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1659]),
[final] ).
cnf(i_0_2780,plain,
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1542]),
[final] ).
cnf(i_0_2781,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Omonom(X1,X2,X3),c_Polynomial_Omonom(X1,X4,X3)) = c_Polynomial_Omonom(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1660]),
[final] ).
cnf(i_0_2782,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Omonom(X1,X2,X3),c_Polynomial_Omonom(X1,X4,X3)) = c_Polynomial_Omonom(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1661]),
[final] ).
cnf(i_0_2783,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1662]),
[final] ).
cnf(i_0_2784,plain,
( c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1663]),
[final] ).
cnf(i_0_2785,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1664]),
[final] ).
cnf(i_0_2786,plain,
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk15_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_1665]),
[final] ).
cnf(i_0_2787,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1666]),
[final] ).
cnf(i_0_2788,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1667]),
[final] ).
cnf(i_0_2789,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[i_0_1668,c_0_1401]),
[final] ).
cnf(i_0_2790,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1669]),
[final] ).
cnf(i_0_2791,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2792,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_OpCons(X1,X3,X4)) = c_Polynomial_OpCons(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2793,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2794,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2795,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2796,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_1675]),
[final] ).
cnf(i_0_2797,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_1676]),
[final] ).
cnf(i_0_2798,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2799,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2800,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_1678,c_0_1401]),
[final] ).
cnf(i_0_2801,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[i_0_1679,c_0_1401]),
[final] ).
cnf(i_0_2802,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1680]),
[final] ).
cnf(i_0_2803,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1681]),
[final] ).
cnf(i_0_2804,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1682]),
[final] ).
cnf(i_0_2805,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1683]),
[final] ).
cnf(i_0_2806,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1684]),
[final] ).
cnf(i_0_2807,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1685]),
[final] ).
cnf(i_0_2808,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1686]),
[final] ).
cnf(i_0_2809,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1687]),
[final] ).
cnf(i_0_2810,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1688]),
[final] ).
cnf(i_0_2811,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_2812,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_2813,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_2814,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_2815,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_2816,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_2817,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1521]),
[final] ).
cnf(i_0_2818,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1695]),
[final] ).
cnf(i_0_2819,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1696]),
[final] ).
cnf(i_0_2820,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_2821,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_2822,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_2823,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Groups_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1698]),
[final] ).
cnf(i_0_2824,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1699]),
[final] ).
cnf(i_0_2825,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1700]),
[final] ).
cnf(i_0_2826,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1701]),
[final] ).
cnf(i_0_2827,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[i_0_1702]),
[final] ).
cnf(i_0_2828,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X2,X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_2829,plain,
( X1 = c_Polynomial_Osynthetic__div(X2,X3,X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X3,c_Polynomial_Osmult(X2,X4,X1)) != c_Polynomial_OpCons(X2,X5,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_2830,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),c_Divides_Odiv__class_Odiv(X1,X3,X2)) = c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X2)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1705]),
[final] ).
cnf(i_0_2831,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk34_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_2832,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(rw,[status(thm)],[i_0_1707,c_0_1401]),
[final] ).
cnf(i_0_2833,plain,
( c_Polynomial_Osynthetic__div(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X3),X4),c_Polynomial_Osynthetic__div(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1708]),
[final] ).
cnf(i_0_2834,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3)),X4) = hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1709]),
[final] ).
cnf(i_0_2835,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1710,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2836,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1711]),
[final] ).
cnf(i_0_2837,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_2838,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1580]),
[final] ).
cnf(i_0_2839,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1713]),
[final] ).
cnf(i_0_2840,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ 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,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_2841,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_2842,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))
| ~ 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,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_2843,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1715]),
[final] ).
cnf(i_0_2844,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2845,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_2846,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1583]),
[final] ).
cnf(i_0_2847,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_2848,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_2849,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1589]),
[final] ).
cnf(i_0_2850,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_2851,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1718]),
[final] ).
cnf(i_0_2852,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_2853,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ 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_1718]),
[final] ).
cnf(i_0_2854,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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_2855,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4))
| ~ 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_1720]),
[final] ).
cnf(i_0_2856,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_2857,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1722]),
[final] ).
cnf(i_0_2858,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_2859,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_2860,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1725]),
[final] ).
cnf(i_0_2861,plain,
( X1 = hAPP(c_Polynomial_Opoly(X2,X3),X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X3,c_Polynomial_Osmult(X2,X4,X5)) != c_Polynomial_OpCons(X2,X1,X5)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_2862,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_2863,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_2864,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1727]),
[final] ).
cnf(i_0_2865,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1728]),
[final] ).
cnf(i_0_2866,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_2867,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_2868,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Osmult(X1,X2,X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1730]),
[final] ).
cnf(i_0_2869,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),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_2870,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_2871,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_2872,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_2873,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_2874,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_2875,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_2876,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_2877,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1733]),
[final] ).
cnf(i_0_2878,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1734]),
[final] ).
cnf(i_0_2879,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_2880,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_2881,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1737]),
[final] ).
cnf(i_0_2882,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Opcompose(X1,X2,X3)),X4) = hAPP(c_Polynomial_Opoly(X1,X2),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_2883,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_2884,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_2885,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_2886,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),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_1741,c_0_1401]),
[final] ).
cnf(i_0_2887,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,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_1742,c_0_1401]),
[final] ).
cnf(i_0_2888,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1743,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2889,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1744,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2890,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_1745]),
[final] ).
cnf(i_0_2891,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_1746]),
[final] ).
cnf(i_0_2892,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_1747]),
[final] ).
cnf(i_0_2893,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_1748]),
[final] ).
cnf(i_0_2894,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_1749]),
[final] ).
cnf(i_0_2895,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_1750]),
[final] ).
cnf(i_0_2896,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_1751]),
[final] ).
cnf(i_0_2897,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_1752]),
[final] ).
cnf(i_0_2898,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3),X1)),esk37_2(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1753]),
[final] ).
cnf(i_0_2899,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_1754]),
[final] ).
cnf(i_0_2900,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_2901,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1756]),
[final] ).
cnf(i_0_2902,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_2903,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1758]),
[final] ).
cnf(i_0_2904,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1759]),
[final] ).
cnf(i_0_2905,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1760]),
[final] ).
cnf(i_0_2906,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1761]),
[final] ).
cnf(i_0_2907,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1762]),
[final] ).
cnf(i_0_2908,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1763]),
[final] ).
cnf(i_0_2909,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_2910,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1763]),
[final] ).
cnf(i_0_2911,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_2912,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_2913,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_2914,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1766]),
[final] ).
cnf(i_0_2915,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ 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_1767]),
[final] ).
cnf(i_0_2916,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ 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_1768]),
[final] ).
cnf(i_0_2917,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ 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)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_2918,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ 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)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1769]),
[final] ).
cnf(i_0_2919,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ 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_1770]),
[final] ).
cnf(i_0_2920,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ 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))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_2921,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring(X1)
| ~ 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_1771]),
[final] ).
cnf(i_0_2922,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ 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))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1769]),
[final] ).
cnf(i_0_2923,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_1772]),
[final] ).
cnf(i_0_2924,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_1607]),
[final] ).
cnf(i_0_2925,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_1773]),
[final] ).
cnf(i_0_2926,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_1609]),
[final] ).
cnf(i_0_2927,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_1774]),
[final] ).
cnf(i_0_2928,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_1612]),
[final] ).
cnf(i_0_2929,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_1775]),
[final] ).
cnf(i_0_2930,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_1614]),
[final] ).
cnf(i_0_2931,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),X2) = X3
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_2932,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_2933,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1778,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2934,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1779,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2935,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1780,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2936,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1781]),
[final] ).
cnf(i_0_2937,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_2938,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_2939,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1620]),
[final] ).
cnf(i_0_2940,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1783]),
[final] ).
cnf(i_0_2941,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_1784]),
[final] ).
cnf(i_0_2942,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_1785]),
[final] ).
cnf(i_0_2943,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_1786]),
[final] ).
cnf(i_0_2944,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_1787]),
[final] ).
cnf(i_0_2945,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_1788]),
[final] ).
cnf(i_0_2946,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1789]),
[final] ).
cnf(i_0_2947,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1790]),
[final] ).
cnf(i_0_2948,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)),
inference(split_conjunct,[status(thm)],[i_0_1791]),
[final] ).
cnf(i_0_2949,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_2950,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_1793]),
[final] ).
cnf(i_0_2951,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_1629]),
[final] ).
cnf(i_0_2952,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_2953,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1795]),
[final] ).
cnf(i_0_2954,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1796]),
[final] ).
cnf(i_0_2955,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_1797]),
[final] ).
cnf(i_0_2956,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_1630]),
[final] ).
cnf(i_0_2957,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1798]),
[final] ).
cnf(i_0_2958,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk17_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1799,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2959,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_1800,c_0_1401]),
[final] ).
cnf(i_0_2960,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_2961,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_2962,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2) = c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1803]),
[final] ).
cnf(i_0_2963,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X3,X2),X2) = c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1804]),
[final] ).
cnf(i_0_2964,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_1805,c_0_1401]),
[final] ).
cnf(i_0_2965,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_1806,c_0_1401]),
[final] ).
cnf(i_0_2966,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk17_2(X1,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_1807,c_0_1401]),
[final] ).
cnf(i_0_2967,plain,
( c_Polynomial_Omonom(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),c_Polynomial_Omonom(X1,X2,X3))
| ~ class_Groups_Ozero(X1) ),
inference(rw,[status(thm)],[i_0_1808,c_0_1401]),
[final] ).
cnf(i_0_2968,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_2969,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_2970,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_2971,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_2972,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1727]),
[final] ).
cnf(i_0_2973,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X3,X4)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X3),X4)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_2974,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X4)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1813]),
[final] ).
cnf(i_0_2975,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X4)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_2976,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1815,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2977,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1816,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_2978,plain,
( X1 = X3
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_2979,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_2980,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,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(split_conjunct,[status(thm)],[i_0_1819]),
[final] ).
cnf(i_0_2981,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_2982,plain,
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,c_RealDef_Oreal(tc_Nat_Onat,X1))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1820]),
[final] ).
cnf(i_0_2983,plain,
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,c_RealDef_Oreal(tc_Nat_Onat,X1))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1821]),
[final] ).
cnf(i_0_2984,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1822]),
[final] ).
cnf(i_0_2985,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_1823]),
[final] ).
cnf(i_0_2986,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_1824]),
[final] ).
cnf(i_0_2987,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_1825]),
[final] ).
cnf(i_0_2988,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_1826]),
[final] ).
cnf(i_0_2989,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_1827]),
[final] ).
cnf(i_0_2990,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1828,c_0_1401]),
[final] ).
cnf(i_0_2991,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_1829]),
[final] ).
cnf(i_0_2992,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_1830]),
[final] ).
cnf(i_0_2993,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_1831]),
[final] ).
cnf(i_0_2994,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_1832]),
[final] ).
cnf(i_0_2995,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_1833]),
[final] ).
cnf(i_0_2996,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_2997,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1834]),
[final] ).
cnf(i_0_2998,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1835]),
[final] ).
cnf(i_0_2999,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1836]),
[final] ).
cnf(i_0_3000,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_3001,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1838,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3002,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1839]),
[final] ).
cnf(i_0_3003,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1840]),
[final] ).
cnf(i_0_3004,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1841,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3005,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1842,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3006,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
inference(rw,[status(thm)],[i_0_1843,c_0_1401]),
[final] ).
cnf(i_0_3007,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_Omonom(X1,X3,X4)) = c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3008,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1845]),
[final] ).
cnf(i_0_3009,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1846]),
[final] ).
cnf(i_0_3010,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))
| ~ 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(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_3011,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1848]),
[final] ).
cnf(i_0_3012,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1849]),
[final] ).
cnf(i_0_3013,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Power_Opower(X1) ),
inference(rw,[status(thm)],[i_0_1850,c_0_1401]),
[final] ).
cnf(i_0_3014,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_1851,c_0_1401]),
[final] ).
cnf(i_0_3015,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_1852,c_0_1401]),
[final] ).
cnf(i_0_3016,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))),
inference(split_conjunct,[status(thm)],[i_0_1853]),
[final] ).
cnf(i_0_3017,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1854,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3018,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1855,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3019,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1685]),
[final] ).
cnf(i_0_3020,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X3))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1688]),
[final] ).
cnf(i_0_3021,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X3))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_3022,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3023,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X4,X5) != c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3024,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3025,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X4,X5) != c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3026,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1858]),
[final] ).
cnf(i_0_3027,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),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_1859]),
[final] ).
cnf(i_0_3028,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1687]),
[final] ).
cnf(i_0_3029,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1584]),
[final] ).
cnf(i_0_3030,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1860]),
[final] ).
cnf(i_0_3031,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_3032,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1861]),
[final] ).
cnf(i_0_3033,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1862]),
[final] ).
cnf(i_0_3034,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1701]),
[final] ).
cnf(i_0_3035,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1702]),
[final] ).
cnf(i_0_3036,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3037,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
inference(split_conjunct,[status(thm)],[i_0_1864]),
[final] ).
cnf(i_0_3038,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1865]),
[final] ).
cnf(i_0_3039,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1866]),
[final] ).
cnf(i_0_3040,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1867]),
[final] ).
cnf(i_0_3041,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_1868]),
[final] ).
cnf(i_0_3042,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3043,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_1870]),
[final] ).
cnf(i_0_3044,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1871]),
[final] ).
cnf(i_0_3045,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_1872,c_0_1401]),
[final] ).
cnf(i_0_3046,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_1873,c_0_1401]),
[final] ).
cnf(i_0_3047,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_1874,c_0_1401]),
[final] ).
cnf(i_0_3048,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_1875,c_0_1401]),
[final] ).
cnf(i_0_3049,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1876]),
[final] ).
cnf(i_0_3050,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_1877,c_0_1401]),
[final] ).
cnf(i_0_3051,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_1878,c_0_1401]),
[final] ).
cnf(i_0_3052,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_1879,c_0_1401]),
[final] ).
cnf(i_0_3053,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_1880,c_0_1401]),
[final] ).
cnf(i_0_3054,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,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_1881,c_0_1401]),
[final] ).
cnf(i_0_3055,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_3056,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3057,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_1884,c_0_1401]),
[final] ).
cnf(i_0_3058,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1885]),
[final] ).
cnf(i_0_3059,plain,
( c_Rings_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1886]),
[final] ).
cnf(i_0_3060,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[i_0_1887,c_0_1401]),
[final] ).
cnf(i_0_3061,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1888]),
[final] ).
cnf(i_0_3062,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1889]),
[final] ).
cnf(i_0_3063,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1890]),
[final] ).
cnf(i_0_3064,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3065,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3066,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1893,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3067,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_1894]),
[final] ).
cnf(i_0_3068,plain,
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3069,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_3070,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_1897]),
[final] ).
cnf(i_0_3071,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_1898]),
[final] ).
cnf(i_0_3072,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_1898]),
[final] ).
cnf(i_0_3073,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_1899]),
[final] ).
cnf(i_0_3074,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_1900]),
[final] ).
cnf(i_0_3075,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_3076,plain,
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_RealDef_Oreal(tc_Nat_Onat,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1902]),
[final] ).
cnf(i_0_3077,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(rw,[status(thm)],[i_0_1903,c_0_1401]),
[final] ).
cnf(i_0_3078,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[i_0_1904,c_0_1401]),
[final] ).
cnf(i_0_3079,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1905,c_0_1401]),c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3080,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1906,c_0_1401]),c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3081,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk18_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1907,c_0_1401]),
[final] ).
cnf(i_0_3082,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_1908]),
[final] ).
cnf(i_0_3083,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_1908]),
[final] ).
cnf(i_0_3084,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_1909]),
[final] ).
cnf(i_0_3085,plain,
( c_Divides_Odiv__class_Odiv(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2) = c_Groups_Ouminus__class_Ouminus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2))
| ~ class_Divides_Oring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1910]),
[final] ).
cnf(i_0_3086,plain,
( c_Divides_Odiv__class_Odiv(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2))
| ~ class_Divides_Oring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1911]),
[final] ).
cnf(i_0_3087,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1912,c_0_1401]),c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3088,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X4),X3)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3089,plain,
( X2 = 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)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_3090,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_3091,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_3092,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1584]),
[final] ).
cnf(i_0_3093,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3094,plain,
( c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_3095,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_3096,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_3097,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1836]),
[final] ).
cnf(i_0_3098,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_3099,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1834]),
[final] ).
cnf(i_0_3100,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1835]),
[final] ).
cnf(i_0_3101,plain,
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X3,X2)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1915]),
[final] ).
cnf(i_0_3102,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X3,X2)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1916]),
[final] ).
cnf(i_0_3103,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X3) = c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1917]),
[final] ).
cnf(i_0_3104,plain,
( X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3105,plain,
( X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_3106,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_3107,plain,
( c_Rings_Odvd__class_Odvd(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1620]),
[final] ).
cnf(i_0_3108,plain,
( c_Rings_Odvd__class_Odvd(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_3109,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1888]),
[final] ).
cnf(i_0_3110,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1889]),
[final] ).
cnf(i_0_3111,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_1908]),
[final] ).
cnf(i_0_3112,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1919]),
[final] ).
cnf(i_0_3113,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1920]),
[final] ).
cnf(i_0_3114,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_1825]),
[final] ).
cnf(i_0_3115,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_1826]),
[final] ).
cnf(i_0_3116,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_1827]),
[final] ).
cnf(i_0_3117,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_1823]),
[final] ).
cnf(i_0_3118,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_1824]),
[final] ).
cnf(i_0_3119,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_1921,c_0_1401]),
[final] ).
cnf(i_0_3120,plain,
( X3 = X4
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3121,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3122,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1924]),
[final] ).
cnf(i_0_3123,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3124,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_1926,c_0_1401]),
[final] ).
cnf(i_0_3125,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1927]),
[final] ).
cnf(i_0_3126,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1928]),
[final] ).
cnf(i_0_3127,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1929]),
[final] ).
cnf(i_0_3128,plain,
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1930]),
[final] ).
cnf(i_0_3129,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_3130,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1932,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3131,plain,
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3132,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_1909]),
[final] ).
cnf(i_0_3133,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1839]),
[final] ).
cnf(i_0_3134,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1840]),
[final] ).
cnf(i_0_3135,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_1934]),
[final] ).
cnf(i_0_3136,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1935]),
[final] ).
cnf(i_0_3137,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3138,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1924]),
[final] ).
cnf(i_0_3139,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1936]),
[final] ).
cnf(i_0_3140,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk15_2(X2,X3))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1665]),
[final] ).
cnf(i_0_3141,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3142,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,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3143,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rw,[status(thm)],[i_0_1939,c_0_1401]),
[final] ).
cnf(i_0_3144,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[i_0_1940,c_0_1401]),
[final] ).
cnf(i_0_3145,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[i_0_1941,c_0_1401]),
[final] ).
cnf(i_0_3146,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1942]),
[final] ).
cnf(i_0_3147,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Odiv(X1,X3,X2)) = X3
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1943]),
[final] ).
cnf(i_0_3148,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1944,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3149,plain,
( c_Rings_Odvd__class_Odvd(X2,X3,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3150,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3)) = c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3151,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3)) = c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3152,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk25_3(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1418]),
[final] ).
cnf(i_0_3153,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rw,[status(thm)],[i_0_1948,c_0_1401]),
[final] ).
cnf(i_0_3154,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1949]),
[final] ).
cnf(i_0_3155,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1950]),
[final] ).
cnf(i_0_3156,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1951]),
[final] ).
cnf(i_0_3157,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_1754]),
[final] ).
cnf(i_0_3158,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_1754]),
[final] ).
cnf(i_0_3159,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_3160,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1952]),
[final] ).
cnf(i_0_3161,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1953]),
[final] ).
cnf(i_0_3162,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1876]),
[final] ).
cnf(i_0_3163,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1954,c_0_1401]),
[final] ).
cnf(i_0_3164,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1955,c_0_1401]),
[final] ).
cnf(i_0_3165,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1956,c_0_1401]),
[final] ).
cnf(i_0_3166,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1871]),
[final] ).
cnf(i_0_3167,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3168,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1957,c_0_1401]),
[final] ).
cnf(i_0_3169,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1958,c_0_1401]),
[final] ).
cnf(i_0_3170,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1959,c_0_1401]),
[final] ).
cnf(i_0_3171,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1960,c_0_1401]),
[final] ).
cnf(i_0_3172,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_3173,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1961,c_0_1401]),
[final] ).
cnf(i_0_3174,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_1962,c_0_1401]),
[final] ).
cnf(i_0_3175,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_1963]),
[final] ).
cnf(i_0_3176,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_1964]),
[final] ).
cnf(i_0_3177,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1890]),
[final] ).
cnf(i_0_3178,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3179,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3180,plain,
( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X3,X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1919]),
[final] ).
cnf(i_0_3181,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3182,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1966]),
[final] ).
cnf(i_0_3183,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1967]),
[final] ).
cnf(i_0_3184,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_1968]),
[final] ).
cnf(i_0_3185,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_1969]),
[final] ).
cnf(i_0_3186,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_1404]),
[final] ).
cnf(i_0_3187,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3188,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_3189,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_1971]),
[final] ).
cnf(i_0_3190,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_1972]),
[final] ).
cnf(i_0_3191,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_1973]),
[final] ).
cnf(i_0_3192,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_1974]),
[final] ).
cnf(i_0_3193,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_1975]),
[final] ).
cnf(i_0_3194,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_1976]),
[final] ).
cnf(i_0_3195,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_1977]),
[final] ).
cnf(i_0_3196,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_1978]),
[final] ).
cnf(i_0_3197,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1979,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3198,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1980,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3199,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1981,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3200,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1982,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3201,plain,
( X2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,X3) != X4
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1983]),
[final] ).
cnf(i_0_3202,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1687]),
[final] ).
cnf(i_0_3203,plain,
( X2 = X3
| c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1916]),
[final] ).
cnf(i_0_3204,plain,
( c_Divides_Odiv__class_Odiv(X2,X1,X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
| ~ c_Rings_Odvd__class_Odvd(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1983]),
[final] ).
cnf(i_0_3205,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X2)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1858]),
[final] ).
cnf(i_0_3206,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),X2)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1859]),
[final] ).
cnf(i_0_3207,plain,
( c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1915]),
[final] ).
cnf(i_0_3208,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1984]),
[final] ).
cnf(i_0_3209,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_3210,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_3211,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_3212,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1986]),
[final] ).
cnf(i_0_3213,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_3214,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_3215,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_1989]),
[final] ).
cnf(i_0_3216,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_1990]),
[final] ).
cnf(i_0_3217,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_1991]),
[final] ).
cnf(i_0_3218,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_1992]),
[final] ).
cnf(i_0_3219,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_1993]),
[final] ).
cnf(i_0_3220,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_1994]),
[final] ).
cnf(i_0_3221,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_1995]),
[final] ).
cnf(i_0_3222,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_1996]),
[final] ).
cnf(i_0_3223,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1997]),
[final] ).
cnf(i_0_3224,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1998]),
[final] ).
cnf(i_0_3225,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3226,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3227,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3228,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2002]),
[final] ).
cnf(i_0_3229,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2003,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3230,plain,
( 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),X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3231,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2005]),
[final] ).
cnf(i_0_3232,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3233,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2007]),
[final] ).
cnf(i_0_3234,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3235,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_3236,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_3237,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2010]),
[final] ).
cnf(i_0_3238,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2011]),
[final] ).
cnf(i_0_3239,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2012]),
[final] ).
cnf(i_0_3240,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2013]),
[final] ).
cnf(i_0_3241,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2014,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3242,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2015,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3243,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opos__poly(X2,X1)
| ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X3,X1))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1919]),
[final] ).
cnf(i_0_3244,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3) = X2
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3245,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3246,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2017]),
[final] ).
cnf(i_0_3247,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2018]),
[final] ).
cnf(i_0_3248,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2019]),
[final] ).
cnf(i_0_3249,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2020]),
[final] ).
cnf(i_0_3250,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_2021]),
[final] ).
cnf(i_0_3251,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_3252,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_2023,c_0_1401]),
[final] ).
cnf(i_0_3253,plain,
( c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ c_Polynomial_Opos__poly(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_3254,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),
inference(split_conjunct,[status(thm)],[i_0_2025]),
[final] ).
cnf(i_0_3255,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,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[i_0_2026,c_0_1401]),
[final] ).
cnf(i_0_3256,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2027,c_0_1401]),
[final] ).
cnf(i_0_3257,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3258,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_1909]),
[final] ).
cnf(i_0_3259,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2029]),
[final] ).
cnf(i_0_3260,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2029]),
[final] ).
cnf(i_0_3261,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_3262,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_3263,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3264,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3265,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2032]),
[final] ).
cnf(i_0_3266,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2032]),
[final] ).
cnf(i_0_3267,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)),
inference(split_conjunct,[status(thm)],[i_0_2033]),
[final] ).
cnf(i_0_3268,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)),
inference(split_conjunct,[status(thm)],[i_0_2034]),
[final] ).
cnf(i_0_3269,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Omonom(X1,X2,X3)) = c_Polynomial_Omonom(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2035]),
[final] ).
cnf(i_0_3270,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3271,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2037,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3272,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2038,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3273,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2039,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3274,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2040,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3275,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_2041]),
[final] ).
cnf(i_0_3276,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2042]),
[final] ).
cnf(i_0_3277,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2043]),
[final] ).
cnf(i_0_3278,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_3279,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2045]),
[final] ).
cnf(i_0_3280,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2046]),
[final] ).
cnf(i_0_3281,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2047]),
[final] ).
cnf(i_0_3282,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3283,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_2048]),
[final] ).
cnf(i_0_3284,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2049]),
[final] ).
cnf(i_0_3285,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2050]),
[final] ).
cnf(i_0_3286,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_3287,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X4),X3)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3288,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[i_0_2052,c_0_1401]),
[final] ).
cnf(i_0_3289,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3290,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3291,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3292,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2053]),
[final] ).
cnf(i_0_3293,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2002]),
[final] ).
cnf(i_0_3294,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2054,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3295,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_2055]),
[final] ).
cnf(i_0_3296,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))),
inference(split_conjunct,[status(thm)],[i_0_2056]),
[final] ).
cnf(i_0_3297,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3298,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oplus__class_Oplus(X1,X2,X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2057]),
[final] ).
cnf(i_0_3299,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2058]),
[final] ).
cnf(i_0_3300,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2059]),
[final] ).
cnf(i_0_3301,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2060]),
[final] ).
cnf(i_0_3302,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2061]),
[final] ).
cnf(i_0_3303,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2062]),
[final] ).
cnf(i_0_3304,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X2) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2063]),
[final] ).
cnf(i_0_3305,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_2064]),
[final] ).
cnf(i_0_3306,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(rw,[status(thm)],[i_0_2065,c_0_1401]),
[final] ).
cnf(i_0_3307,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_2066]),
[final] ).
cnf(i_0_3308,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_3309,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2045]),
[final] ).
cnf(i_0_3310,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2046]),
[final] ).
cnf(i_0_3311,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2047]),
[final] ).
cnf(i_0_3312,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2067]),
[final] ).
cnf(i_0_3313,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2068]),
[final] ).
cnf(i_0_3314,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2069]),
[final] ).
cnf(i_0_3315,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2070]),
[final] ).
cnf(i_0_3316,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2071]),
[final] ).
cnf(i_0_3317,plain,
( X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3318,plain,
( c_Polynomial_Opos__poly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ c_Polynomial_Opos__poly(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_3319,plain,
( X3 = X4
| X1 != X2
| c_Groups_Ominus__class_Ominus(X5,X1,X2) != c_Groups_Ominus__class_Ominus(X5,X3,X4)
| ~ class_Groups_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_3320,plain,
( X3 = X4
| X1 != X2
| c_Groups_Ominus__class_Ominus(X5,X3,X4) != c_Groups_Ominus__class_Ominus(X5,X1,X2)
| ~ class_Groups_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_3321,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(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_2058]),
[final] ).
cnf(i_0_3322,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(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_2059]),
[final] ).
cnf(i_0_3323,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ 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_2060]),
[final] ).
cnf(i_0_3324,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ 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_2061]),
[final] ).
cnf(i_0_3325,plain,
( X2 = 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2075,c_0_1401]),
[final] ).
cnf(i_0_3326,plain,
( X2 = 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,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[i_0_2076,c_0_1401]),
[final] ).
cnf(i_0_3327,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)
| X1 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_3328,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_2078]),
[final] ).
cnf(i_0_3329,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2042]),
[final] ).
cnf(i_0_3330,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2043]),
[final] ).
cnf(i_0_3331,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,X3,X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2079]),
[final] ).
cnf(i_0_3332,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_2080]),
[final] ).
cnf(i_0_3333,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_2081]),
[final] ).
cnf(i_0_3334,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_2082]),
[final] ).
cnf(i_0_3335,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_2083]),
[final] ).
cnf(i_0_3336,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2084]),
[final] ).
cnf(i_0_3337,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_2085]),
[final] ).
cnf(i_0_3338,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X3,X2,X5)
| ~ class_Groups_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_3339,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X4,X1) != c_Polynomial_OpCons(X3,X5,X2)
| ~ class_Groups_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_3340,plain,
( X2 = X4
| c_Polynomial_Omonom(X1,X2,X3) != c_Polynomial_Omonom(X1,X4,X3)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2087]),
[final] ).
cnf(i_0_3341,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_2088]),
[final] ).
cnf(i_0_3342,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_2089]),
[final] ).
cnf(i_0_3343,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_2090]),
[final] ).
cnf(i_0_3344,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_2091]),
[final] ).
cnf(i_0_3345,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_2092]),
[final] ).
cnf(i_0_3346,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_2093]),
[final] ).
cnf(i_0_3347,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_2094]),
[final] ).
cnf(i_0_3348,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_2095]),
[final] ).
cnf(i_0_3349,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_2096]),
[final] ).
cnf(i_0_3350,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_2097]),
[final] ).
cnf(i_0_3351,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_2098]),
[final] ).
cnf(i_0_3352,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_2099]),
[final] ).
cnf(i_0_3353,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_2100]),
[final] ).
cnf(i_0_3354,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_2101]),
[final] ).
cnf(i_0_3355,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_2048]),
[final] ).
cnf(i_0_3356,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2102]),
[final] ).
cnf(i_0_3357,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2103]),
[final] ).
cnf(i_0_3358,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2104,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3359,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2105,c_0_1401]),c_0_1401]),
[final] ).
cnf(i_0_3360,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Oorder(X1,X3,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_3361,plain,
( X1 = X2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2107]),
[final] ).
cnf(i_0_3362,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2108]),
[final] ).
cnf(i_0_3363,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,esk34_1(X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_3364,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_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_2109,c_0_1401]),
[final] ).
cnf(i_0_3365,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2070]),
[final] ).
cnf(i_0_3366,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2071]),
[final] ).
cnf(i_0_3367,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3368,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_3369,plain,
( c_Rings_Odvd__class_Odvd(X2,X1,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3))
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3370,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3371,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2113]),
[final] ).
cnf(i_0_3372,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2114]),
[final] ).
cnf(i_0_3373,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2115]),
[final] ).
cnf(i_0_3374,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2116]),
[final] ).
cnf(i_0_3375,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2117]),
[final] ).
cnf(i_0_3376,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2118]),
[final] ).
cnf(i_0_3377,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_3378,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_3379,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2121]),
[final] ).
cnf(i_0_3380,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_3381,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_2123]),
[final] ).
cnf(i_0_3382,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2124]),
[final] ).
cnf(i_0_3383,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3384,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_3385,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rw,[status(thm)],[i_0_2127,c_0_1401]),
[final] ).
cnf(i_0_3386,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3387,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3388,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_2129,c_0_1401]),
[final] ).
cnf(i_0_3389,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_2130]),
[final] ).
cnf(i_0_3390,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_2131]),
[final] ).
cnf(i_0_3391,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,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_2084]),
[final] ).
cnf(i_0_3392,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(rw,[status(thm)],[i_0_2132,c_0_1401]),
[final] ).
cnf(i_0_3393,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1871]),
[final] ).
cnf(i_0_3394,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_2133,c_0_1401]),
[final] ).
cnf(i_0_3395,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,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_2134,c_0_1401]),
[final] ).
cnf(i_0_3396,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_3397,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2136]),
[final] ).
cnf(i_0_3398,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk6_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2137]),
[final] ).
cnf(i_0_3399,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk5_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2138]),
[final] ).
cnf(i_0_3400,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk15_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_1665]),
[final] ).
cnf(i_0_3401,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_2139,c_0_1401]),
[final] ).
cnf(i_0_3402,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3403,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_3404,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,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_2140]),
[final] ).
cnf(i_0_3405,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
inference(split_conjunct,[status(thm)],[i_0_2141]),
[final] ).
cnf(i_0_3406,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_2142]),
[final] ).
cnf(i_0_3407,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2143]),
[final] ).
cnf(i_0_3408,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_2144]),
[final] ).
cnf(i_0_3409,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_2145]),
[final] ).
cnf(i_0_3410,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2146]),
[final] ).
cnf(i_0_3411,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_2147]),
[final] ).
cnf(i_0_3412,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_3413,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_3414,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk16_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[i_0_2148,c_0_1401]),
[final] ).
cnf(i_0_3415,plain,
( c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X3,X2))
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1919]),
[final] ).
cnf(i_0_3416,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2146]),
[final] ).
cnf(i_0_3417,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2147]),
[final] ).
cnf(i_0_3418,plain,
( X1 = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3419,plain,
( X1 = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_3420,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3421,plain,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2152]),
[final] ).
cnf(i_0_3422,plain,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2153]),
[final] ).
cnf(i_0_3423,plain,
( c_Nat__Transfer_Otsub(X2,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2154]),
[final] ).
cnf(i_0_3424,plain,
( c_Nat__Transfer_Otsub(X2,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2155]),
[final] ).
cnf(i_0_3425,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_2156]),
[final] ).
cnf(i_0_3426,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_2157]),
[final] ).
cnf(i_0_3427,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_2158]),
[final] ).
cnf(i_0_3428,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_2159]),
[final] ).
cnf(i_0_3429,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_2160]),
[final] ).
cnf(i_0_3430,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_2161]),
[final] ).
cnf(i_0_3431,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_2162]),
[final] ).
cnf(i_0_3432,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_2078]),
[final] ).
cnf(i_0_3433,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_2163]),
[final] ).
cnf(i_0_3434,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1984]),
[final] ).
cnf(i_0_3435,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3436,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3437,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2165]),
[final] ).
cnf(i_0_3438,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2166]),
[final] ).
cnf(i_0_3439,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_2156]),
[final] ).
cnf(i_0_3440,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_2157]),
[final] ).
cnf(i_0_3441,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_2048]),
[final] ).
cnf(i_0_3442,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_2167]),
[final] ).
cnf(i_0_3443,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[i_0_2168,c_0_1401]),
[final] ).
cnf(i_0_3444,plain,
( c_Rings_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Rings_Odvd(X1)
| X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_2169]),
[final] ).
cnf(i_0_3445,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2170]),
[final] ).
cnf(i_0_3446,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2170]),
[final] ).
cnf(i_0_3447,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_3448,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(split_conjunct,[status(thm)],[i_0_2172]),
[final] ).
cnf(i_0_3449,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2173]),
[final] ).
cnf(i_0_3450,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,X2,X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2174]),
[final] ).
cnf(i_0_3451,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_3452,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2176]),
[final] ).
cnf(i_0_3453,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2177]),
[final] ).
cnf(i_0_3454,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2178]),
[final] ).
cnf(i_0_3455,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2179]),
[final] ).
cnf(i_0_3456,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3457,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_2181]),
[final] ).
cnf(i_0_3458,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_2182]),
[final] ).
cnf(i_0_3459,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_2183]),
[final] ).
cnf(i_0_3460,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_3461,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_3462,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2179]),
[final] ).
cnf(i_0_3463,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_3464,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),
inference(split_conjunct,[status(thm)],[i_0_2187]),
[final] ).
cnf(i_0_3465,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_2137]),
[final] ).
cnf(i_0_3466,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_2138]),
[final] ).
cnf(i_0_3467,plain,
( c_Polynomial_Omonom(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2188]),
[final] ).
cnf(i_0_3468,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3469,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_2189]),
[final] ).
cnf(i_0_3470,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_2190]),
[final] ).
cnf(i_0_3471,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_2191]),
[final] ).
cnf(i_0_3472,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_2182]),
[final] ).
cnf(i_0_3473,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_2183]),
[final] ).
cnf(i_0_3474,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_3475,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_3476,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2192]),
[final] ).
cnf(i_0_3477,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3478,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[i_0_2193,c_0_1401]),
[final] ).
cnf(i_0_3479,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2194]),
[final] ).
cnf(i_0_3480,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_2195]),
[final] ).
cnf(i_0_3481,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)),
inference(split_conjunct,[status(thm)],[i_0_2196]),
[final] ).
cnf(i_0_3482,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_3483,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3484,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),
inference(split_conjunct,[status(thm)],[i_0_2199]),
[final] ).
cnf(i_0_3485,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2200]),
[final] ).
cnf(i_0_3486,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2201]),
[final] ).
cnf(i_0_3487,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Osmult(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2202]),
[final] ).
cnf(i_0_3488,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2203]),
[final] ).
cnf(i_0_3489,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[i_0_2204]),
[final] ).
cnf(i_0_3490,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2205]),
[final] ).
cnf(i_0_3491,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2205]),
[final] ).
cnf(i_0_3492,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_3493,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_2162]),
[final] ).
cnf(i_0_3494,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_OpCons(X2,X3,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2207]),
[final] ).
cnf(i_0_3495,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2208]),
[final] ).
cnf(i_0_3496,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_2209]),
[final] ).
cnf(i_0_3497,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_2210]),
[final] ).
cnf(i_0_3498,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_2094]),
[final] ).
cnf(i_0_3499,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_2211]),
[final] ).
cnf(i_0_3500,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_2212]),
[final] ).
cnf(i_0_3501,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_2213]),
[final] ).
cnf(i_0_3502,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_2214]),
[final] ).
cnf(i_0_3503,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_2097]),
[final] ).
cnf(i_0_3504,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_2215]),
[final] ).
cnf(i_0_3505,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_2216]),
[final] ).
cnf(i_0_3506,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_2095]),
[final] ).
cnf(i_0_3507,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_2217]),
[final] ).
cnf(i_0_3508,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_2218]),
[final] ).
cnf(i_0_3509,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_2219]),
[final] ).
cnf(i_0_3510,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_2220]),
[final] ).
cnf(i_0_3511,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_3512,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3513,plain,
( X3 = c_Groups_Ouminus__class_Ouminus(X1,X2)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_3514,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X2,X1,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2207]),
[final] ).
cnf(i_0_3515,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2224]),
[final] ).
cnf(i_0_3516,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_2225]),
[final] ).
cnf(i_0_3517,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_2226]),
[final] ).
cnf(i_0_3518,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2227]),
[final] ).
cnf(i_0_3519,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(rw,[status(thm)],[i_0_2228,c_0_1401]),
[final] ).
cnf(i_0_3520,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2229]),
[final] ).
cnf(i_0_3521,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_2230,c_0_1401]),
[final] ).
cnf(i_0_3522,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2231]),
[final] ).
cnf(i_0_3523,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_2232]),
[final] ).
cnf(i_0_3524,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_2233]),
[final] ).
cnf(i_0_3525,plain,
( c_Polynomial_Oorder(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X1,X3),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_3526,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_3527,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2235]),
[final] ).
cnf(i_0_3528,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_2236]),
[final] ).
cnf(i_0_3529,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2237]),
[final] ).
cnf(i_0_3530,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2238]),
[final] ).
cnf(i_0_3531,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2239]),
[final] ).
cnf(i_0_3532,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_3533,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2241]),
[final] ).
cnf(i_0_3534,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3535,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_2243]),
[final] ).
cnf(i_0_3536,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_2244]),
[final] ).
cnf(i_0_3537,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_2245]),
[final] ).
cnf(i_0_3538,plain,
( X2 = X3
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_3539,plain,
( X2 = X3
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3540,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_3541,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3542,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_2250]),
[final] ).
cnf(i_0_3543,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_3544,plain,
( c_Polynomial_OpCons(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2207]),
[final] ).
cnf(i_0_3545,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3546,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2152]),
[final] ).
cnf(i_0_3547,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3548,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2178]),
[final] ).
cnf(i_0_3549,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2205]),
[final] ).
cnf(i_0_3550,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_3551,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2156]),
[final] ).
cnf(i_0_3552,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2094]),
[final] ).
cnf(i_0_3553,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2252]),
[final] ).
cnf(i_0_3554,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2253]),
[final] ).
cnf(i_0_3555,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2254]),
[final] ).
cnf(i_0_3556,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2209]),
[final] ).
cnf(i_0_3557,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2209]),
[final] ).
cnf(i_0_3558,plain,
( c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2255]),
[final] ).
cnf(i_0_3559,plain,
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2256]),
[final] ).
cnf(i_0_3560,plain,
( c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2257]),
[final] ).
cnf(i_0_3561,plain,
( c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2258]),
[final] ).
cnf(i_0_3562,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_3563,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_2259]),
[final] ).
cnf(i_0_3564,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2260]),
[final] ).
cnf(i_0_3565,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_3566,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_2262]),
[final] ).
cnf(i_0_3567,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rw,[status(thm)],[i_0_2263,c_0_1401]),
[final] ).
cnf(i_0_3568,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rw,[status(thm)],[i_0_2264,c_0_1401]),
[final] ).
cnf(i_0_3569,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rw,[status(thm)],[i_0_2265,c_0_1401]),
[final] ).
cnf(i_0_3570,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_2266,c_0_1401]),
[final] ).
cnf(i_0_3571,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_2267,c_0_1401]),
[final] ).
cnf(i_0_3572,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_2268,c_0_1401]),
[final] ).
cnf(i_0_3573,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_3574,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2270]),
[final] ).
cnf(i_0_3575,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2271]),
[final] ).
cnf(i_0_3576,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2272]),
[final] ).
cnf(i_0_3577,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2273]),
[final] ).
cnf(i_0_3578,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2274]),
[final] ).
cnf(i_0_3579,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_2275]),
[final] ).
cnf(i_0_3580,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_2275]),
[final] ).
cnf(i_0_3581,plain,
( c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2276]),
[final] ).
cnf(i_0_3582,plain,
( c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_3583,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2278]),
[final] ).
cnf(i_0_3584,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_3585,plain,
( c_Polynomial_Osmult(X2,X3,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2202]),
[final] ).
cnf(i_0_3586,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2208]),
[final] ).
cnf(i_0_3587,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_2280]),
[final] ).
cnf(i_0_3588,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_pCons_Oprems]),
[final] ).
cnf(i_0_3589,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rw,[status(thm)],[i_0_2281,c_0_1401]),
[final] ).
cnf(i_0_3590,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_2282,c_0_1401]),
[final] ).
cnf(i_0_3591,plain,
( c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3592,plain,
( c_Groups_Oplus__class_Oplus(X2,X3,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_3593,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk24_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1557]),
[final] ).
cnf(i_0_3594,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk23_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1561]),
[final] ).
cnf(i_0_3595,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk9_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1559]),
[final] ).
cnf(i_0_3596,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk8_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1563]),
[final] ).
cnf(i_0_3597,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2283]),
[final] ).
cnf(i_0_3598,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk38_1(X1)))
| v_thesis____ ),
inference(split_conjunct,[status(thm)],[i_0_1422]),
[final] ).
cnf(i_0_3599,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2284]),
[final] ).
cnf(i_0_3600,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_2285]),
[final] ).
cnf(i_0_3601,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_2286]),
[final] ).
cnf(i_0_3602,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_2287]),
[final] ).
cnf(i_0_3603,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_2288]),
[final] ).
cnf(i_0_3604,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1))),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_3605,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2290]),
[final] ).
cnf(i_0_3606,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2291]),
[final] ).
cnf(i_0_3607,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3608,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2183]),
[final] ).
cnf(i_0_3609,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2232]),
[final] ).
cnf(i_0_3610,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2232]),
[final] ).
cnf(i_0_3611,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2292]),
[final] ).
cnf(i_0_3612,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_3613,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_3614,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2294]),
[final] ).
cnf(i_0_3615,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2295]),
[final] ).
cnf(i_0_3616,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_3617,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2284]),
[final] ).
cnf(i_0_3618,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opos__poly(X1,X2)
| c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_3619,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2200]),
[final] ).
cnf(i_0_3620,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_3621,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2299]),
[final] ).
cnf(i_0_3622,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3623,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk37_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1753]),
[final] ).
cnf(i_0_3624,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2203]),
[final] ).
cnf(i_0_3625,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3626,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_3627,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3628,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3629,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_3630,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_3631,plain,
( c_Polynomial_Omonom(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2224]),
[final] ).
cnf(i_0_3632,plain,
( c_Polynomial_Osmult(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2202]),
[final] ).
cnf(i_0_3633,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),
inference(split_conjunct,[status(thm)],[i_0_2305]),
[final] ).
cnf(i_0_3634,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_3635,plain,
( c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3636,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2308]),
[final] ).
cnf(i_0_3637,plain,
( c_Power_Opower__class_Opower(X1) = c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_3638,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3639,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2310]),
[final] ).
cnf(i_0_3640,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_3641,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_3642,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_3643,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_3644,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_2244]),
[final] ).
cnf(i_0_3645,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_2245]),
[final] ).
cnf(i_0_3646,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_2315]),
[final] ).
cnf(i_0_3647,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_2316]),
[final] ).
cnf(i_0_3648,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3649,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2318]),
[final] ).
cnf(i_0_3650,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_3651,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_3652,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2238]),
[final] ).
cnf(i_0_3653,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2238]),
[final] ).
cnf(i_0_3654,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X3),X1,X2)
| X1 != X2
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1916]),
[final] ).
cnf(i_0_3655,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_2250]),
[final] ).
cnf(i_0_3656,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Nat__Transfer_Otsub(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2155]),
[final] ).
cnf(i_0_3657,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_3658,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_3659,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_3660,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2323]),
[final] ).
cnf(i_0_3661,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk22_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1436]),
[final] ).
cnf(i_0_3662,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk7_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1438]),
[final] ).
cnf(i_0_3663,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1666]),
[final] ).
cnf(i_0_3664,plain,
( c_Groups_Ominus__class_Ominus(X3,X1,X2) = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Groups_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_3665,plain,
( c_Groups_Ominus__class_Ominus(X3,X1,X2) = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Groups_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3666,plain,
( hAPP(c_Polynomial_Opoly(X2,X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_3667,plain,
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2324]),
[final] ).
cnf(i_0_3668,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_2325]),
[final] ).
cnf(i_0_3669,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_2326]),
[final] ).
cnf(i_0_3670,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_2327]),
[final] ).
cnf(i_0_3671,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2328]),
[final] ).
cnf(i_0_3672,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_2329]),
[final] ).
cnf(i_0_3673,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_2330]),
[final] ).
cnf(i_0_3674,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_2331]),
[final] ).
cnf(i_0_3675,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[final] ).
cnf(i_0_3676,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2333]),
[final] ).
cnf(i_0_3677,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_2275]),
[final] ).
cnf(i_0_3678,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2334]),
[final] ).
cnf(i_0_3679,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2335]),
[final] ).
cnf(i_0_3680,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2336]),
[final] ).
cnf(i_0_3681,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2337]),
[final] ).
cnf(i_0_3682,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2338]),
[final] ).
cnf(i_0_3683,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2339]),
[final] ).
cnf(i_0_3684,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_3685,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_3686,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2340]),
[final] ).
cnf(i_0_3687,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2157]),
[final] ).
cnf(i_0_3688,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2341]),
[final] ).
cnf(i_0_3689,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2342]),
[final] ).
cnf(i_0_3690,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X1)),
inference(split_conjunct,[status(thm)],[i_0_2343]),
[final] ).
cnf(i_0_3691,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),
inference(split_conjunct,[status(thm)],[i_0_2344]),
[final] ).
cnf(i_0_3692,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_3693,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_2262]),
[final] ).
cnf(i_0_3694,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2345]),
[final] ).
cnf(i_0_3695,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2346]),
[final] ).
cnf(i_0_3696,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_2347,c_0_1401]),
[final] ).
cnf(i_0_3697,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3698,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2348]),
[final] ).
cnf(i_0_3699,plain,
( X2 = X3
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3)
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2349]),
[final] ).
cnf(i_0_3700,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3701,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_3702,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_2259]),
[final] ).
cnf(i_0_3703,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_2350]),
[final] ).
cnf(i_0_3704,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1277]),
[final] ).
cnf(i_0_3705,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_int__0__less__1]),
[final] ).
cnf(i_0_3706,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]),
[final] ).
cnf(i_0_3707,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]),
[final] ).
cnf(i_0_3708,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2351]),
[final] ).
cnf(i_0_3709,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2352]),
[final] ).
cnf(i_0_3710,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_i__mult__eq2]),
[final] ).
cnf(i_0_3711,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2353]),
[final] ).
cnf(i_0_3712,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_2354]),
[final] ).
cnf(i_0_3713,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2355]),
[final] ).
cnf(i_0_3714,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2356]),
[final] ).
cnf(i_0_3715,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_2357]),
[final] ).
cnf(i_0_3716,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2358]),
[final] ).
cnf(i_0_3717,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_3718,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2121]),
[final] ).
cnf(i_0_3719,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2121]),
[final] ).
cnf(i_0_3720,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2190]),
[final] ).
cnf(i_0_3721,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2182]),
[final] ).
cnf(i_0_3722,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2359]),
[final] ).
cnf(i_0_3723,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_3724,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_2360]),
[final] ).
cnf(i_0_3725,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_2361]),
[final] ).
cnf(i_0_3726,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_2362]),
[final] ).
cnf(i_0_3727,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_2363]),
[final] ).
cnf(i_0_3728,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2364]),
[final] ).
cnf(i_0_3729,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2365]),
[final] ).
cnf(i_0_3730,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2366]),
[final] ).
cnf(i_0_3731,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_3732,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1504]),
[final] ).
cnf(i_0_3733,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_3734,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_3735,plain,
( X2 = X3
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2367]),
[final] ).
cnf(i_0_3736,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2368]),
[final] ).
cnf(i_0_3737,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2369]),
[final] ).
cnf(i_0_3738,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2370]),
[final] ).
cnf(i_0_3739,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2371]),
[final] ).
cnf(i_0_3740,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2372]),
[final] ).
cnf(i_0_3741,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2373]),
[final] ).
cnf(i_0_3742,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2374]),
[final] ).
cnf(i_0_3743,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2375]),
[final] ).
cnf(i_0_3744,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2376]),
[final] ).
cnf(i_0_3745,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2377]),
[final] ).
cnf(i_0_3746,plain,
( X1 = X2
| ~ hBOOL(c_fequal(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2378]),
[final] ).
cnf(i_0_3747,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2379]),
[final] ).
cnf(i_0_3748,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X3) = X2
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2380]),
[final] ).
cnf(i_0_3749,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X3) = X2
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2380]),
[final] ).
cnf(i_0_3750,plain,
( X3 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2381]),
[final] ).
cnf(i_0_3751,plain,
( X3 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2381]),
[final] ).
cnf(i_0_3752,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2382]),
[final] ).
cnf(i_0_3753,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2382]),
[final] ).
cnf(i_0_3754,plain,
( X1 = X2
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_RealDef_Oreal(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2383]),
[final] ).
cnf(i_0_3755,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2384]),
[final] ).
cnf(i_0_3756,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2385]),
[final] ).
cnf(i_0_3757,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2386]),
[final] ).
cnf(i_0_3758,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2387]),
[final] ).
cnf(i_0_3759,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2388]),
[final] ).
cnf(i_0_3760,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2389]),
[final] ).
cnf(i_0_3761,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2390]),
[final] ).
cnf(i_0_3762,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) != X2
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2391]),
[final] ).
cnf(i_0_3763,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X1)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2392]),
[final] ).
cnf(i_0_3764,plain,
( hBOOL(c_fequal(X1,X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2393]),
[final] ).
cnf(i_0_3765,plain,
( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2385]),
[final] ).
cnf(i_0_3766,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| c_Groups_Ozero__class_Ozero(X1) != X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2384]),
[final] ).
cnf(i_0_3767,plain,
( c_RealVector_Onorm__class_Onorm(X2,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2386]),
[final] ).
cnf(i_0_3768,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2394]),
[final] ).
cnf(i_0_3769,plain,
( c_Groups_Ouminus__class_Ouminus(X2,X1) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2391]),
[final] ).
cnf(i_0_3770,plain,
( X1 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2392]),
[final] ).
cnf(i_0_3771,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2395]),
[final] ).
cnf(i_0_3772,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2396]),
[final] ).
cnf(i_0_3773,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2397]),
[final] ).
cnf(i_0_3774,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2398]),
[final] ).
cnf(i_0_3775,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2399]),
[final] ).
cnf(i_0_3776,plain,
( c_RealDef_Oreal(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2399]),
[final] ).
cnf(i_0_3777,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_2400]),
[final] ).
cnf(i_0_3778,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_2401]),
[final] ).
cnf(i_0_3779,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__1]),
[final] ).
cnf(i_0_3780,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__zero]),
[final] ).
cnf(i_0_3781,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_zminus__0]),
[final] ).
cnf(i_0_3782,plain,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2402]),
[final] ).
cnf(i_0_3783,plain,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2403]),
[final] ).
cnf(i_0_3784,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2404]),
[final] ).
cnf(i_0_3785,plain,
( class_Rings_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2405]),
[final] ).
cnf(i_0_3786,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2406]),
[final] ).
cnf(i_0_3787,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2407]),
[final] ).
cnf(i_0_3788,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2408]),
[final] ).
cnf(i_0_3789,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2409]),
[final] ).
cnf(i_0_3790,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2410]),
[final] ).
cnf(i_0_3791,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2411]),
[final] ).
cnf(i_0_3792,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2412]),
[final] ).
cnf(i_0_3793,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2413]),
[final] ).
cnf(i_0_3794,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2414]),
[final] ).
cnf(i_0_3795,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2415]),
[final] ).
cnf(i_0_3796,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2416]),
[final] ).
cnf(i_0_3797,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2417]),
[final] ).
cnf(i_0_3798,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2418]),
[final] ).
cnf(i_0_3799,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2419]),
[final] ).
cnf(i_0_3800,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2420]),
[final] ).
cnf(i_0_3801,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2421]),
[final] ).
cnf(i_0_3802,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2422]),
[final] ).
cnf(i_0_3803,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2423]),
[final] ).
cnf(i_0_3804,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2424]),
[final] ).
cnf(i_0_3805,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2425]),
[final] ).
cnf(i_0_3806,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2426]),
[final] ).
cnf(i_0_3807,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2427]),
[final] ).
cnf(i_0_3808,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2428]),
[final] ).
cnf(i_0_3809,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2429]),
[final] ).
cnf(i_0_3810,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2430]),
[final] ).
cnf(i_0_3811,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2431]),
[final] ).
cnf(i_0_3812,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2432]),
[final] ).
cnf(i_0_3813,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2433]),
[final] ).
cnf(i_0_3814,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2434]),
[final] ).
cnf(i_0_3815,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2435]),
[final] ).
cnf(i_0_3816,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2436]),
[final] ).
cnf(i_0_3817,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2437]),
[final] ).
cnf(i_0_3818,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2438]),
[final] ).
cnf(i_0_3819,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2439]),
[final] ).
cnf(i_0_3820,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2440]),
[final] ).
cnf(i_0_3821,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2441]),
[final] ).
cnf(i_0_3822,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2442]),
[final] ).
cnf(i_0_3823,plain,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2443]),
[final] ).
cnf(i_0_3824,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2444]),
[final] ).
cnf(i_0_3825,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2445]),
[final] ).
cnf(i_0_3826,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2446]),
[final] ).
cnf(i_0_3827,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2447]),
[final] ).
cnf(i_0_3828,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2448]),
[final] ).
cnf(i_0_3829,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2449]),
[final] ).
cnf(i_0_3830,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2450]),
[final] ).
cnf(i_0_3831,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2451]),
[final] ).
cnf(i_0_3832,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2452]),
[final] ).
cnf(i_0_3833,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2453]),
[final] ).
cnf(i_0_3834,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2454]),
[final] ).
cnf(i_0_3835,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2455]),
[final] ).
cnf(i_0_3836,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2456]),
[final] ).
cnf(i_0_3837,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2457]),
[final] ).
cnf(i_0_3838,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2458]),
[final] ).
cnf(i_0_3839,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_assms]),
[final] ).
cnf(i_0_3840,plain,
v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_H]),
[final] ).
cnf(i_0_3841,plain,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_natceiling__one]),
[final] ).
cnf(i_0_3842,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_natceiling__zero]),
[final] ).
cnf(i_0_3843,plain,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_natfloor__one]),
[final] ).
cnf(i_0_3844,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_natfloor__zero]),
[final] ).
cnf(i_0_3845,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__0__neq__1]),
[final] ).
cnf(i_0_3846,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__zero__not__eq__one]),
[final] ).
cnf(i_0_3847,plain,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_complex__i__not__one]),
[final] ).
cnf(i_0_3848,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_complex__i__not__zero]),
[final] ).
cnf(i_0_3849,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__comm__monoid__add]),
[final] ).
cnf(i_0_3850,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__comm__monoid__add]),
[final] ).
cnf(i_0_3851,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add]),
[final] ).
cnf(i_0_3852,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add]),
[final] ).
cnf(i_0_3853,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]),
[final] ).
cnf(i_0_3854,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
[final] ).
cnf(i_0_3855,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
[final] ).
cnf(i_0_3856,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]),
[final] ).
cnf(i_0_3857,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]),
[final] ).
cnf(i_0_3858,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]),
[final] ).
cnf(i_0_3859,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]),
[final] ).
cnf(i_0_3860,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odvd]),
[final] ).
cnf(i_0_3861,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odvd]),
[final] ).
cnf(i_0_3862,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3863,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3864,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3865,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3866,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_3867,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_3868,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Power_Opower]),
[final] ).
cnf(i_0_3869,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]),
[final] ).
cnf(i_0_3870,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_3871,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_3872,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_3873,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]),
[final] ).
cnf(i_0_3874,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]),
[final] ).
cnf(i_0_3875,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]),
[final] ).
cnf(i_0_3876,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]),
[final] ).
cnf(i_0_3877,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1]),
[final] ).
cnf(i_0_3878,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
[final] ).
cnf(i_0_3879,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]),
[final] ).
cnf(i_0_3880,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]),
[final] ).
cnf(i_0_3881,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3882,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3883,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3884,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_3885,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_3886,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_3887,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_3888,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_3889,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_3890,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]),
[final] ).
cnf(i_0_3891,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict]),
[final] ).
cnf(i_0_3892,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3893,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3894,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3895,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3896,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_3897,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_3898,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_3899,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_3900,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_3901,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_3902,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_3903,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_3904,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_3905,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_3906,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_3907,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]),
[final] ).
cnf(i_0_3908,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]),
[final] ).
cnf(i_0_3909,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_3910,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_3911,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]),
[final] ).
cnf(i_0_3912,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]),
[final] ).
cnf(i_0_3913,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_3914,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_3915,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3916,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3917,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3918,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_3919,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_3920,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_3921,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3922,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3923,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3924,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_3925,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_3926,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_3927,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_3928,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_3929,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]),
[final] ).
cnf(i_0_3930,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]),
[final] ).
cnf(i_0_3931,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3932,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3933,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3934,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3935,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_3936,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_3937,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]),
[final] ).
cnf(i_0_3938,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]),
[final] ).
cnf(i_0_3939,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]),
[final] ).
cnf(i_0_3940,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__no__zero__divisors]),
[final] ).
cnf(i_0_3941,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors]),
[final] ).
cnf(i_0_3942,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_3943,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_3944,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_3945,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_3946,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_3947,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_3948,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]),
[final] ).
cnf(i_0_3949,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]),
[final] ).
cnf(i_0_3950,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_3951,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]),
[final] ).
cnf(i_0_3952,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]),
[final] ).
cnf(i_0_3953,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]),
[final] ).
cnf(i_0_3954,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3955,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3956,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3957,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra]),
[final] ).
cnf(i_0_3958,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]),
[final] ).
cnf(i_0_3959,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_3960,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_3961,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_3962,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_3963,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3964,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3965,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3966,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]),
[final] ).
cnf(i_0_3967,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]),
[final] ).
cnf(i_0_3968,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]),
[final] ).
cnf(i_0_3969,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
[final] ).
cnf(i_0_3970,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]),
[final] ).
cnf(i_0_3971,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]),
[final] ).
cnf(i_0_3972,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]),
[final] ).
cnf(i_0_3973,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]),
[final] ).
cnf(i_0_3974,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_3975,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_3976,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_3977,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_3978,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
[final] ).
cnf(i_0_3979,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_3980,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
[final] ).
cnf(i_0_3981,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
[final] ).
cnf(i_0_3982,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_3983,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_3984,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_3985,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_3986,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_3987,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_3988,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_3989,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_3990,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_3991,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_3992,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_3993,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_3994,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_3995,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
[final] ).
cnf(i_0_3996,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_3997,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]),
[final] ).
cnf(i_0_3998,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_3999,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
[final] ).
cnf(i_0_4000,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_4001,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]),
[final] ).
cnf(i_0_4002,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_4003,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_4004,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]),
[final] ).
cnf(i_0_4005,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_4006,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_4007,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_4008,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
[final] ).
cnf(i_0_4009,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]),
[final] ).
cnf(i_0_4010,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]),
[final] ).
cnf(i_0_4011,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]),
[final] ).
cnf(i_0_4012,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Oring__char__0]),
[final] ).
cnf(i_0_4013,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]),
[final] ).
cnf(i_0_4014,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]),
[final] ).
cnf(i_0_4015,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]),
[final] ).
cnf(i_0_4016,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4017,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4018,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4019,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4020,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_4021,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_4022,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]),
[final] ).
cnf(i_0_4023,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]),
[final] ).
cnf(i_0_4024,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_4025,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_4026,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_4027,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_4028,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_4029,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_4030,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_4031,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_4032,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_4033,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_4034,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]),
[final] ).
cnf(i_0_4035,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]),
[final] ).
cnf(i_0_4036,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__0]),
[final] ).
cnf(i_0_4037,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]),
[final] ).
cnf(i_0_4038,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_4039,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
[final] ).
cnf(i_0_4040,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_4041,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]),
[final] ).
cnf(i_0_4042,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]),
[final] ).
cnf(i_0_4043,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]),
[final] ).
cnf(i_0_4044,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[i_0_2459]),
[final] ).
cnf(i_0_4045,axiom,
X1 = X1 ).
cnf(i_0_4046,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4047,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4048,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_4049,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_4050,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_4051,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_4052,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_4053,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_4054,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_4055,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_4056,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_4057,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X1,X3,X4) = c_Polynomial_Osynthetic__div(X2,X3,X4) ) ).
cnf(i_0_4058,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X1,X4) = c_Polynomial_Osynthetic__div(X3,X2,X4) ) ).
cnf(i_0_4059,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X4,X1) = c_Polynomial_Osynthetic__div(X3,X4,X2) ) ).
cnf(i_0_4060,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_4061,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_4062,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_4063,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_4064,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_4065,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_4066,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_4067,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_4068,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_4069,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_4070,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_4071,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_4072,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4073,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_4074,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_4075,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_4076,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X3,X4) ) ).
cnf(i_0_4077,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X4) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X4) ) ).
cnf(i_0_4078,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X4,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X4,X2) ) ).
cnf(i_0_4079,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_4080,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_4081,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_4082,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X1,X3,X4) = c_Polynomial_Opcompose(X2,X3,X4) ) ).
cnf(i_0_4083,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X1,X4) = c_Polynomial_Opcompose(X3,X2,X4) ) ).
cnf(i_0_4084,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X4,X1) = c_Polynomial_Opcompose(X3,X4,X2) ) ).
cnf(i_0_4085,axiom,
( X1 != X2
| c_Polynomial_Omonom(X1,X3,X4) = c_Polynomial_Omonom(X2,X3,X4) ) ).
cnf(i_0_4086,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X1,X4) = c_Polynomial_Omonom(X3,X2,X4) ) ).
cnf(i_0_4087,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X4,X1) = c_Polynomial_Omonom(X3,X4,X2) ) ).
cnf(i_0_4088,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_4089,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_4090,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_4091,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_4092,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_4093,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_4094,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_4095,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_4096,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_4097,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X1,X3,X4,X5,X6) = c_Polynomial_Opoly__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_4098,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X1,X4,X5,X6) = c_Polynomial_Opoly__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_4099,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X4,X1,X5,X6) = c_Polynomial_Opoly__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_4100,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X4,X5,X1,X6) = c_Polynomial_Opoly__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_4101,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X4,X5,X6,X1) = c_Polynomial_Opoly__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_4102,axiom,
( X1 != X2
| c_Polynomial_OpCons(X1,X3,X4) = c_Polynomial_OpCons(X2,X3,X4) ) ).
cnf(i_0_4103,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X1,X4) = c_Polynomial_OpCons(X3,X2,X4) ) ).
cnf(i_0_4104,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X4,X2) ) ).
cnf(i_0_4105,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4106,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4107,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4108,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4109,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4110,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_4111,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4112,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4113,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4114,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4115,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4116,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4117,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4118,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4119,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4120,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4121,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4122,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4123,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4124,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4125,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4126,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4127,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_4128,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4129,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4130,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4131,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4132,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4133,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4134,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4135,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4136,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4137,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4138,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4139,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4140,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4141,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4142,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4143,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4144,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4145,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4146,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4147,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4148,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4149,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4150,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4151,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4152,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4153,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4154,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_4155,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X2,X3) ) ).
cnf(i_0_4156,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X3,X1)
| c_Polynomial_Opos__poly(X3,X2) ) ).
cnf(i_0_4157,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4158,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4159,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4160,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4161,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4162,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4163,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4164,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4165,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4166,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4167,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4168,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4169,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4170,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4171,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4172,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4173,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4174,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| c_Rings_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_4175,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X4)
| c_Rings_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_4176,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X4,X1)
| c_Rings_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_4177,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4178,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4045_001,axiom,
X1 = X1 ).
cnf(i_0_4046_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4047_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4048_004,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_4049_005,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_4050_006,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_4051_007,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_4052_008,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_4053_009,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_4054_010,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_4055_011,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_4056_012,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_4057_013,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X1,X3,X4) = c_Polynomial_Osynthetic__div(X2,X3,X4) ) ).
cnf(i_0_4058_014,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X1,X4) = c_Polynomial_Osynthetic__div(X3,X2,X4) ) ).
cnf(i_0_4059_015,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X4,X1) = c_Polynomial_Osynthetic__div(X3,X4,X2) ) ).
cnf(i_0_4060_016,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_4061_017,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_4062_018,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_4063_019,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_4064_020,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_4065_021,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_4066_022,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_4067_023,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_4068_024,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_4069_025,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_4070_026,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_4071_027,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_4072_028,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4073_029,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_4074_030,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_4075_031,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_4076_032,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X3,X4) ) ).
cnf(i_0_4077_033,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X4) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X4) ) ).
cnf(i_0_4078_034,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X4,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X4,X2) ) ).
cnf(i_0_4079_035,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_4080_036,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_4081_037,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_4082_038,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X1,X3,X4) = c_Polynomial_Opcompose(X2,X3,X4) ) ).
cnf(i_0_4083_039,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X1,X4) = c_Polynomial_Opcompose(X3,X2,X4) ) ).
cnf(i_0_4084_040,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X4,X1) = c_Polynomial_Opcompose(X3,X4,X2) ) ).
cnf(i_0_4085_041,axiom,
( X1 != X2
| c_Polynomial_Omonom(X1,X3,X4) = c_Polynomial_Omonom(X2,X3,X4) ) ).
cnf(i_0_4086_042,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X1,X4) = c_Polynomial_Omonom(X3,X2,X4) ) ).
cnf(i_0_4087_043,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X4,X1) = c_Polynomial_Omonom(X3,X4,X2) ) ).
cnf(i_0_4088_044,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_4089_045,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_4090_046,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_4091_047,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_4092_048,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_4093_049,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_4094_050,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_4095_051,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_4096_052,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_4097_053,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X1,X3,X4,X5,X6) = c_Polynomial_Opoly__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_4098_054,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X1,X4,X5,X6) = c_Polynomial_Opoly__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_4099_055,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X4,X1,X5,X6) = c_Polynomial_Opoly__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_4100_056,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X4,X5,X1,X6) = c_Polynomial_Opoly__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_4101_057,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X4,X5,X6,X1) = c_Polynomial_Opoly__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_4102_058,axiom,
( X1 != X2
| c_Polynomial_OpCons(X1,X3,X4) = c_Polynomial_OpCons(X2,X3,X4) ) ).
cnf(i_0_4103_059,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X1,X4) = c_Polynomial_OpCons(X3,X2,X4) ) ).
cnf(i_0_4104_060,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X4,X2) ) ).
cnf(i_0_4105_061,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4106_062,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4107_063,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4108_064,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4109_065,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4110_066,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_4111_067,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4112_068,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4113_069,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4114_070,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4115_071,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4116_072,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4117_073,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4118_074,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4119_075,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4120_076,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4121_077,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4122_078,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4123_079,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4124_080,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4125_081,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4126_082,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4127_083,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_4128_084,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4129_085,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4130_086,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4131_087,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4132_088,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4133_089,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4134_090,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4135_091,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4136_092,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4137_093,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4138_094,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4139_095,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4140_096,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4141_097,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4142_098,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4143_099,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4144_100,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4145_101,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4146_102,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4147_103,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4148_104,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4149_105,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4150_106,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4151_107,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4152_108,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4153_109,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4154_110,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_4155_111,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X2,X3) ) ).
cnf(i_0_4156_112,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X3,X1)
| c_Polynomial_Opos__poly(X3,X2) ) ).
cnf(i_0_4157_113,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4158_114,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4159_115,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4160_116,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4161_117,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4162_118,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4163_119,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4164_120,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4165_121,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4166_122,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4167_123,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4168_124,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4169_125,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4170_126,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4171_127,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4172_128,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4173_129,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4174_130,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| c_Rings_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_4175_131,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X4)
| c_Rings_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_4176_132,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X4,X1)
| c_Rings_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_4177_133,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4178_134,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4179,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(equality_inference,[],[2503]) ).
cnf(i_0_4180,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1)) ),
inference(equality_inference,[],[2504]) ).
cnf(i_0_4181,plain,
( ~ class_Rings_Oidom(X1)
| X2 = X2
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(equality_inference,[],[2513]) ).
cnf(i_0_4182,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4)) ),
inference(equality_inference,[],[2515]) ).
cnf(i_0_4183,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) ),
inference(equality_inference,[],[2516]) ).
cnf(i_0_4184,plain,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4)) ),
inference(equality_inference,[],[2517]) ).
cnf(i_0_4185,plain,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X5) ),
inference(equality_inference,[],[2518]) ).
cnf(i_0_4186,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),X3) = X3 ),
inference(equality_inference,[],[2528]) ).
cnf(i_0_4187,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X3),X2) ),
inference(equality_inference,[],[2529]) ).
cnf(i_0_4188,plain,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X2)),X3),X4) = X4 ),
inference(equality_inference,[],[2530]) ).
cnf(i_0_4189,plain,
( ~ class_Rings_Oring(X1)
| X2 = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X3)),X4),X2) ),
inference(equality_inference,[],[2531]) ).
cnf(i_0_4190,plain,
X1 = X1,
inference(equality_inference,[],[2549]) ).
cnf(i_0_4191,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X3
| X4 = X4 ),
inference(equality_inference,[],[2552]) ).
cnf(i_0_4192,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),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_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),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_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(equality_inference,[],[2553]) ).
cnf(i_0_4193,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ 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),X2) ),
inference(equality_inference,[],[2567]) ).
cnf(i_0_4194,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(equality_inference,[],[2666]) ).
cnf(i_0_4195,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X3))) ),
inference(equality_inference,[],[2702]) ).
cnf(i_0_4196,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) ),
inference(equality_inference,[],[2731]) ).
cnf(i_0_4197,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X2)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X3)
| ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X3,X3) = c_Divides_Odiv__class_Odiv(X1,X2,X2) ),
inference(equality_inference,[],[2735]) ).
cnf(i_0_4198,plain,
( X1 = X1
| ~ class_Rings_Olinordered__semidom(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),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(equality_inference,[],[2744]) ).
cnf(i_0_4199,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(equality_inference,[],[2977]) ).
cnf(i_0_4200,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(equality_inference,[],[2978]) ).
cnf(i_0_4201,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),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_inference,[],[3060]) ).
cnf(i_0_4202,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_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3079]) ).
cnf(i_0_4203,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_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3080]) ).
cnf(i_0_4204,plain,
( ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(equality_inference,[],[3088]) ).
cnf(i_0_4205,plain,
( ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(equality_inference,[],[3093]) ).
cnf(i_0_4206,plain,
( ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(equality_inference,[],[3107]) ).
cnf(i_0_4207,plain,
( ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(equality_inference,[],[3108]) ).
cnf(i_0_4208,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(equality_inference,[],[3120]) ).
cnf(i_0_4209,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) ),
inference(equality_inference,[],[3180]) ).
cnf(i_0_4210,plain,
( c_Groups_Ozero__class_Ozero(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_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3197]) ).
cnf(i_0_4211,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3198]) ).
cnf(i_0_4212,plain,
( c_Groups_Ozero__class_Ozero(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_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3199]) ).
cnf(i_0_4213,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3200]) ).
cnf(i_0_4214,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),X2) ),
inference(equality_inference,[],[3201]) ).
cnf(i_0_4215,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(equality_inference,[],[3202]) ).
cnf(i_0_4216,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2) = X3 ),
inference(equality_inference,[],[3204]) ).
cnf(i_0_4217,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),X1) ),
inference(equality_inference,[],[3205]) ).
cnf(i_0_4218,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(equality_inference,[],[3206]) ).
cnf(i_0_4219,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(equality_inference,[],[3208]) ).
cnf(i_0_4220,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(equality_inference,[],[3209]) ).
cnf(i_0_4221,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X1) = X2 ),
inference(equality_inference,[],[3244]) ).
cnf(i_0_4222,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1) ),
inference(equality_inference,[],[3245]) ).
cnf(i_0_4223,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(equality_inference,[],[3294]) ).
cnf(i_0_4224,plain,
( ~ class_Rings_Oidom(X1)
| X2 = X2
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(equality_inference,[],[3317]) ).
cnf(i_0_4225,plain,
( c_Groups_Oone__class_Oone(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(equality_inference,[],[3325]) ).
cnf(i_0_4226,plain,
( c_Groups_Oone__class_Oone(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(equality_inference,[],[3326]) ).
cnf(i_0_4227,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3338]) ).
cnf(i_0_4228,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3339]) ).
cnf(i_0_4229,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3340]) ).
cnf(i_0_4230,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[3342]) ).
cnf(i_0_4231,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[3343]) ).
cnf(i_0_4232,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[3345]) ).
cnf(i_0_4233,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2)) ),
inference(equality_inference,[],[3369]) ).
cnf(i_0_4234,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,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_inference,[],[3388]) ).
cnf(i_0_4235,plain,
X1 = X1,
inference(equality_inference,[],[3389]) ).
cnf(i_0_4236,plain,
X1 = X1,
inference(equality_inference,[],[3390]) ).
cnf(i_0_4237,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(equality_inference,[],[3393]) ).
cnf(i_0_4238,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_inference,[],[3394]) ).
cnf(i_0_4239,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[3413]) ).
cnf(i_0_4240,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3418]) ).
cnf(i_0_4241,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3419]) ).
cnf(i_0_4242,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3421]) ).
cnf(i_0_4243,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3422]) ).
cnf(i_0_4244,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,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_inference,[],[3443]) ).
cnf(i_0_4245,plain,
( ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(equality_inference,[],[3444]) ).
cnf(i_0_4246,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1))) ),
inference(equality_inference,[],[3447]) ).
cnf(i_0_4247,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(equality_inference,[],[3466]) ).
cnf(i_0_4248,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) ),
inference(equality_inference,[],[3477]) ).
cnf(i_0_4249,plain,
X1 = X1,
inference(equality_inference,[],[3486]) ).
cnf(i_0_4250,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,[],[3493]) ).
cnf(i_0_4251,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),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_Oone__class_Oone(tc_Nat_Onat)),
inference(equality_inference,[],[3521]) ).
cnf(i_0_4252,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),
inference(equality_inference,[],[3546]) ).
cnf(i_0_4253,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3547]) ).
cnf(i_0_4254,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(equality_inference,[],[3548]) ).
cnf(i_0_4255,plain,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3549]) ).
cnf(i_0_4256,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3550]) ).
cnf(i_0_4257,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3554]) ).
cnf(i_0_4258,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3555]) ).
cnf(i_0_4259,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3556]) ).
cnf(i_0_4260,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3557]) ).
cnf(i_0_4261,plain,
( ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(equality_inference,[],[3585]) ).
cnf(i_0_4262,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(equality_inference,[],[3586]) ).
cnf(i_0_4263,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3587]) ).
cnf(i_0_4264,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3591]) ).
cnf(i_0_4265,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3592]) ).
cnf(i_0_4266,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_inference,[],[3607]) ).
cnf(i_0_4267,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3611]) ).
cnf(i_0_4268,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3612]) ).
cnf(i_0_4269,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3613]) ).
cnf(i_0_4270,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(equality_inference,[],[3619]) ).
cnf(i_0_4271,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_inference,[],[3624]) ).
cnf(i_0_4272,plain,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(equality_inference,[],[3631]) ).
cnf(i_0_4273,plain,
( ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(equality_inference,[],[3632]) ).
cnf(i_0_4274,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_inference,[],[3638]) ).
cnf(i_0_4275,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,[],[3644]) ).
cnf(i_0_4276,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,[],[3645]) ).
cnf(i_0_4277,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3651]) ).
cnf(i_0_4278,plain,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3652]) ).
cnf(i_0_4279,plain,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3653]) ).
cnf(i_0_4280,plain,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X2) ),
inference(equality_inference,[],[3654]) ).
cnf(i_0_4281,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,[],[3655]) ).
cnf(i_0_4282,plain,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3663]) ).
cnf(i_0_4283,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3664]) ).
cnf(i_0_4284,plain,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3665]) ).
cnf(i_0_4285,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3666]) ).
cnf(i_0_4286,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3685]) ).
cnf(i_0_4287,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3686]) ).
cnf(i_0_4288,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3687]) ).
cnf(i_0_4289,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(equality_inference,[],[3697]) ).
cnf(i_0_4290,plain,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| X2 = X2 ),
inference(equality_inference,[],[3699]) ).
cnf(i_0_4291,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(equality_inference,[],[3704]) ).
cnf(i_0_4292,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3718]) ).
cnf(i_0_4293,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3719]) ).
cnf(i_0_4294,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3722]) ).
cnf(i_0_4295,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3723]) ).
cnf(i_0_4296,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(equality_inference,[],[3731]) ).
cnf(i_0_4297,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[3733]) ).
cnf(i_0_4298,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[3734]) ).
cnf(i_0_4299,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3735]) ).
cnf(i_0_4300,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2 ),
inference(equality_inference,[],[3749]) ).
cnf(i_0_4301,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(equality_inference,[],[3751]) ).
cnf(i_0_4302,plain,
( ~ class_Groups_Ozero(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3753]) ).
cnf(i_0_4303,plain,
X1 = X1,
inference(equality_inference,[],[3754]) ).
cnf(i_0_4304,plain,
hBOOL(c_fequal(X1,X1)),
inference(equality_inference,[],[3764]) ).
cnf(i_0_4305,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3765]) ).
cnf(i_0_4306,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[3766]) ).
cnf(i_0_4307,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3767]) ).
cnf(i_0_4308,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3769]) ).
cnf(i_0_4309,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[3770]) ).
cnf(i_0_4310,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_inference,[],[3776]) ).
cnf(i_0_4311,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),esk38_1(X1)))),
inference(scs_inference,[],[i_0_4044,i_0_2492]) ).
cnf(i_0_4312,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,esk2_2(X1,X2),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,v_cs____)),X3))) ),
inference(scs_inference,[],[i_0_3840,i_0_2521]) ).
cnf(i_0_4313,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk38_1(X1))),
inference(scs_inference,[],[i_0_4044,i_0_3598]) ).
cnf(i_0_4314,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1))),
inference(scs_inference,[],[i_0_3742,i_0_3357]) ).
cnf(i_0_4315,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4316,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2)) ),
inference(rename_variables,[],[i_0_3357]) ).
cnf(i_0_4317,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_3742,i_0_4315,i_0_3357,i_0_3416]) ).
cnf(i_0_4318,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4319,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1)) ),
inference(rename_variables,[],[i_0_3416]) ).
cnf(i_0_4320,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk37_2(X1,X2)),
inference(scs_inference,[],[i_0_3742,i_0_4315,i_0_3623,i_0_3357,i_0_3416,i_0_3475]) ).
cnf(i_0_4321,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(rename_variables,[],[i_0_3475]) ).
cnf(i_0_4322,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_3742,i_0_4315,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826]) ).
cnf(i_0_4323,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1))),
inference(rename_variables,[],[i_0_3604]) ).
cnf(i_0_4324,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_2826]) ).
cnf(i_0_4325,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),X1),
inference(scs_inference,[],[i_0_3741,i_0_3742,i_0_4315,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852]) ).
cnf(i_0_4326,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_4327,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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
inference(rename_variables,[],[i_0_2852]) ).
cnf(i_0_4328,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)),
inference(scs_inference,[],[i_0_3741,i_0_4326,i_0_3742,i_0_4315,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854]) ).
cnf(i_0_4329,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_4330,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(rename_variables,[],[i_0_2854]) ).
cnf(i_0_4331,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940]) ).
cnf(i_0_4332,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_4333,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(rename_variables,[],[i_0_2940]) ).
cnf(i_0_4334,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_Oone__class_Oone(tc_Nat_Onat)),X2),X1),
inference(scs_inference,[],[i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964]) ).
cnf(i_0_4335,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_3408]) ).
cnf(i_0_4336,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_2964]) ).
cnf(i_0_4337,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,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053]) ).
cnf(i_0_4338,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_3408]) ).
cnf(i_0_4339,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3053]) ).
cnf(i_0_4340,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055]) ).
cnf(i_0_4341,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4342,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3055]) ).
cnf(i_0_4343,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056]) ).
cnf(i_0_4344,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3056]) ).
cnf(i_0_4345,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_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_4338,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073]) ).
cnf(i_0_4346,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_3408]) ).
cnf(i_0_4347,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_3073]) ).
cnf(i_0_4348,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_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074]) ).
cnf(i_0_4349,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_3408]) ).
cnf(i_0_4350,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_3074]) ).
cnf(i_0_4351,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_4266,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3604,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167]) ).
cnf(i_0_4352,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4266]) ).
cnf(i_0_4353,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3167]) ).
cnf(i_0_4354,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,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),
inference(scs_inference,[],[i_0_4266,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3604,i_0_3176,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171]) ).
cnf(i_0_4355,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_3176]) ).
cnf(i_0_4356,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3171]) ).
cnf(i_0_4357,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_4266,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3604,i_0_3176,i_0_3623,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172]) ).
cnf(i_0_4358,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3172]) ).
cnf(i_0_4359,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4266,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3604,i_0_3176,i_0_3623,i_0_3569,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181]) ).
cnf(i_0_4360,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_3569]) ).
cnf(i_0_4361,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3181]) ).
cnf(i_0_4362,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_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(scs_inference,[],[i_0_4266,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_3604,i_0_3176,i_0_3623,i_0_3569,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194]) ).
cnf(i_0_4363,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rename_variables,[],[i_0_3143]) ).
cnf(i_0_4364,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_3194]) ).
cnf(i_0_4365,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_Oone__class_Oone(tc_Nat_Onat)),X2),
inference(scs_inference,[],[i_0_4266,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_3176,i_0_3623,i_0_3569,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196]) ).
cnf(i_0_4366,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rename_variables,[],[i_0_3143]) ).
cnf(i_0_4367,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_3196]) ).
cnf(i_0_4368,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1))),
inference(scs_inference,[],[i_0_4266,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3176,i_0_3623,i_0_3569,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277]) ).
cnf(i_0_4369,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1))),
inference(rename_variables,[],[i_0_3604]) ).
cnf(i_0_4370,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3277]) ).
cnf(i_0_4371,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)),X1),
inference(scs_inference,[],[i_0_4266,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3176,i_0_3623,i_0_3569,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356]) ).
cnf(i_0_4372,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4373,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2) ),
inference(rename_variables,[],[i_0_3356]) ).
cnf(i_0_4374,plain,
~ class_Groups_Ogroup__add(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4266,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3176,i_0_3623,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384]) ).
cnf(i_0_4375,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_3569]) ).
cnf(i_0_4376,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3384]) ).
cnf(i_0_4377,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) != X1,
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3176,i_0_3623,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393]) ).
cnf(i_0_4378,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4266]) ).
cnf(i_0_4379,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != X2 ),
inference(rename_variables,[],[i_0_3393]) ).
cnf(i_0_4380,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) != X1,
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3175,i_0_3176,i_0_3623,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394]) ).
cnf(i_0_4381,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_3175]) ).
cnf(i_0_4382,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != X2 ),
inference(rename_variables,[],[i_0_3394]) ).
cnf(i_0_4383,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3175,i_0_3176,i_0_3623,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410]) ).
cnf(i_0_4384,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(rename_variables,[],[i_0_3410]) ).
cnf(i_0_4385,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3175,i_0_3176,i_0_3623,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411]) ).
cnf(i_0_4386,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rename_variables,[],[i_0_3411]) ).
cnf(i_0_4387,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3175,i_0_3176,i_0_3623,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417]) ).
cnf(i_0_4388,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4389,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rename_variables,[],[i_0_3417]) ).
cnf(i_0_4390,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3175,i_0_3176,i_0_3623,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446]) ).
cnf(i_0_4391,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4392,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
inference(rename_variables,[],[i_0_3446]) ).
cnf(i_0_4393,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_3175,i_0_3176,i_0_3623,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455]) ).
cnf(i_0_4394,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
inference(rename_variables,[],[i_0_3405]) ).
cnf(i_0_4395,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3455]) ).
cnf(i_0_4396,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_3175,i_0_3176,i_0_3623,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466]) ).
cnf(i_0_4397,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4398,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_3466]) ).
cnf(i_0_4399,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_3175,i_0_3176,i_0_3623,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468]) ).
cnf(i_0_4400,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3468]) ).
cnf(i_0_4401,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_3175,i_0_3176,i_0_3623,i_0_3124,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473]) ).
cnf(i_0_4402,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_3473]) ).
cnf(i_0_4403,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,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_3175,i_0_3176,i_0_3623,i_0_3124,i_0_3569,i_0_4360,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528]) ).
cnf(i_0_4404,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_3528]) ).
cnf(i_0_4405,plain,
~ class_Groups_Oab__group__add(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_3175,i_0_3176,i_0_3623,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577]) ).
cnf(i_0_4406,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_3569]) ).
cnf(i_0_4407,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
inference(rename_variables,[],[i_0_3577]) ).
cnf(i_0_4408,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != X1,
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_3175,i_0_3176,i_0_3623,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600]) ).
cnf(i_0_4409,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4410,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_3600]) ).
cnf(i_0_4411,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_3175,i_0_3176,i_0_3623,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607]) ).
cnf(i_0_4412,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3607]) ).
cnf(i_0_4413,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611]) ).
cnf(i_0_4414,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(rename_variables,[],[i_0_3611]) ).
cnf(i_0_4415,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612]) ).
cnf(i_0_4416,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3612]) ).
cnf(i_0_4417,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != esk37_2(X1,X2),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613]) ).
cnf(i_0_4418,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3613]) ).
cnf(i_0_4419,plain,
c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X1,X1),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695]) ).
cnf(i_0_4420,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(rename_variables,[],[i_0_3695]) ).
cnf(i_0_4421,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1),X2) = X2,
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704]) ).
cnf(i_0_4422,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2 ),
inference(rename_variables,[],[i_0_3704]) ).
cnf(i_0_4423,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != X2,
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722]) ).
cnf(i_0_4424,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3722]) ).
cnf(i_0_4425,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),X3)),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182]) ).
cnf(i_0_4426,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4)) ),
inference(rename_variables,[],[i_0_4182]) ).
cnf(i_0_4427,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183]) ).
cnf(i_0_4428,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) ),
inference(rename_variables,[],[i_0_4183]) ).
cnf(i_0_4429,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),X3) = X3,
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186]) ).
cnf(i_0_4430,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),X3) = X3 ),
inference(rename_variables,[],[i_0_4186]) ).
cnf(i_0_4431,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X2)),X3),X1),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187]) ).
cnf(i_0_4432,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X3),X2) ),
inference(rename_variables,[],[i_0_4187]) ).
cnf(i_0_4433,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1),X1),
inference(scs_inference,[],[i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222]) ).
cnf(i_0_4434,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1) ),
inference(rename_variables,[],[i_0_4222]) ).
cnf(i_0_4435,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046]) ).
cnf(i_0_4436,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067]) ).
cnf(i_0_4437,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X2,
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068]) ).
cnf(i_0_4438,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,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_2887,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721]) ).
cnf(i_0_4439,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,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_2887]) ).
cnf(i_0_4440,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_2721]) ).
cnf(i_0_4441,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2887,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853]) ).
cnf(i_0_4442,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_3401]) ).
cnf(i_0_4443,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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(rename_variables,[],[i_0_2853]) ).
cnf(i_0_4444,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2887,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949]) ).
cnf(i_0_4445,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
inference(rename_variables,[],[i_0_2949]) ).
cnf(i_0_4446,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2887,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965]) ).
cnf(i_0_4447,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_2965]) ).
cnf(i_0_4448,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997]) ).
cnf(i_0_4449,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rename_variables,[],[i_0_3226]) ).
cnf(i_0_4450,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(rename_variables,[],[i_0_2997]) ).
cnf(i_0_4451,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060]) ).
cnf(i_0_4452,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(rename_variables,[],[i_0_3535]) ).
cnf(i_0_4453,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3060]) ).
cnf(i_0_4454,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_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070]) ).
cnf(i_0_4455,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),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_2886]) ).
cnf(i_0_4456,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_3070]) ).
cnf(i_0_4457,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk25_3(X1,X2,esk37_2(X3,X4))),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152]) ).
cnf(i_0_4458,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk25_3(X2,X3,X1)) ),
inference(rename_variables,[],[i_0_3152]) ).
cnf(i_0_4459,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166]) ).
cnf(i_0_4460,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4266]) ).
cnf(i_0_4461,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3166]) ).
cnf(i_0_4462,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177]) ).
cnf(i_0_4463,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3177]) ).
cnf(i_0_4464,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187]) ).
cnf(i_0_4465,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_3187]) ).
cnf(i_0_4466,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_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190]) ).
cnf(i_0_4467,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_3175]) ).
cnf(i_0_4468,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_3190]) ).
cnf(i_0_4469,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_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192]) ).
cnf(i_0_4470,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_3175]) ).
cnf(i_0_4471,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_3192]) ).
cnf(i_0_4472,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_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),X3)),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256]) ).
cnf(i_0_4473,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3256]) ).
cnf(i_0_4474,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276]) ).
cnf(i_0_4475,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3276]) ).
cnf(i_0_4476,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388]) ).
cnf(i_0_4477,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_3175]) ).
cnf(i_0_4478,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3388]) ).
cnf(i_0_4479,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443]) ).
cnf(i_0_4480,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rename_variables,[],[i_0_3443]) ).
cnf(i_0_4481,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X2)),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587]) ).
cnf(i_0_4482,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_3587]) ).
cnf(i_0_4483,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X1),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3974,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694]) ).
cnf(i_0_4484,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X2) ),
inference(rename_variables,[],[i_0_3694]) ).
cnf(i_0_4485,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3974,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217]) ).
cnf(i_0_4486,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),X1) ),
inference(rename_variables,[],[i_0_4217]) ).
cnf(i_0_4487,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3974,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218]) ).
cnf(i_0_4488,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rename_variables,[],[i_0_4218]) ).
cnf(i_0_4489,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Int_Oint),X2,X2),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3974,i_0_3999,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465]) ).
cnf(i_0_4490,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4491,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk3_4(X3,X2,X4,X1)),hAPP(X3,esk3_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_2465]) ).
cnf(i_0_4492,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X4)),X2),X3))),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3974,i_0_3999,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469]) ).
cnf(i_0_4493,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4494,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2469]) ).
cnf(i_0_4495,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2)),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3974,i_0_3999,i_0_4028,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717]) ).
cnf(i_0_4496,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_2717]) ).
cnf(i_0_4497,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X2)),X3),X1)),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3974,i_0_3999,i_0_4027,i_0_4028,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719]) ).
cnf(i_0_4498,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_2719]) ).
cnf(i_0_4499,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3999,i_0_4027,i_0_4028,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003]) ).
cnf(i_0_4500,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3003]) ).
cnf(i_0_4501,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3999,i_0_4014,i_0_4027,i_0_4028,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118]) ).
cnf(i_0_4502,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4503,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_3118]) ).
cnf(i_0_4504,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3999,i_0_4014,i_0_4027,i_0_4028,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121]) ).
cnf(i_0_4505,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4506,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2) ),
inference(rename_variables,[],[i_0_3121]) ).
cnf(i_0_4507,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3999,i_0_4014,i_0_4027,i_0_4028,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137]) ).
cnf(i_0_4508,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4509,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_4510,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_RComplete_Onatfloor(X1)) ),
inference(rename_variables,[],[i_0_3137]) ).
cnf(i_0_4511,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X1),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3999,i_0_4014,i_0_4027,i_0_4028,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262]) ).
cnf(i_0_4512,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4513,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3262]) ).
cnf(i_0_4514,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3999,i_0_4014,i_0_4027,i_0_4028,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309]) ).
cnf(i_0_4515,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4516,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3309]) ).
cnf(i_0_4517,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3999,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322]) ).
cnf(i_0_4518,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4519,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3322]) ).
cnf(i_0_4520,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350]) ).
cnf(i_0_4521,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_3350]) ).
cnf(i_0_4522,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355]) ).
cnf(i_0_4523,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_3355]) ).
cnf(i_0_4524,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382]) ).
cnf(i_0_4525,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),
inference(rename_variables,[],[i_0_3633]) ).
cnf(i_0_4526,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3382]) ).
cnf(i_0_4527,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440]) ).
cnf(i_0_4528,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_3440]) ).
cnf(i_0_4529,plain,
c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685]) ).
cnf(i_0_4530,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X1) ),
inference(rename_variables,[],[i_0_3685]) ).
cnf(i_0_4531,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686]) ).
cnf(i_0_4532,plain,
( ~ class_Orderings_Opreorder(X1)
| X2 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3686]) ).
cnf(i_0_4533,plain,
c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_3143,i_0_4363,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687]) ).
cnf(i_0_4534,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X1,X2) ),
inference(rename_variables,[],[i_0_3687]) ).
cnf(i_0_4535,plain,
~ c_Orderings_Oord__class_Oless__eq(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117]) ).
cnf(i_0_4536,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4537,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118]) ).
cnf(i_0_4538,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(rename_variables,[],[i_0_3534]) ).
cnf(i_0_4539,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119]) ).
cnf(i_0_4540,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rename_variables,[],[i_0_3143]) ).
cnf(i_0_4541,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X1)),X2),X4)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X4)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471]) ).
cnf(i_0_4542,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4543,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2471]) ).
cnf(i_0_4544,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)),X3),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472]) ).
cnf(i_0_4545,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_3176]) ).
cnf(i_0_4546,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(rename_variables,[],[i_0_2472]) ).
cnf(i_0_4547,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473]) ).
cnf(i_0_4548,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(rename_variables,[],[i_0_2473]) ).
cnf(i_0_4549,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X2)),X3),X1)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474]) ).
cnf(i_0_4550,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4551,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(rename_variables,[],[i_0_2474]) ).
cnf(i_0_4552,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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),X3)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475]) ).
cnf(i_0_4553,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(rename_variables,[],[i_0_2475]) ).
cnf(i_0_4554,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),X3),X3),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479]) ).
cnf(i_0_4555,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4556,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2479]) ).
cnf(i_0_4557,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X2)),X3),X1)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481]) ).
cnf(i_0_4558,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4559,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2481]) ).
cnf(i_0_4560,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482]) ).
cnf(i_0_4561,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(rename_variables,[],[i_0_2482]) ).
cnf(i_0_4562,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),X2),X2),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483]) ).
cnf(i_0_4563,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_4564,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3726]) ).
cnf(i_0_4565,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(rename_variables,[],[i_0_2483]) ).
cnf(i_0_4566,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X2)),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X1))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3409,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485]) ).
cnf(i_0_4567,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_3409]) ).
cnf(i_0_4568,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(rename_variables,[],[i_0_2485]) ).
cnf(i_0_4569,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X3)),X2))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3409,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517]) ).
cnf(i_0_4570,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_4271]) ).
cnf(i_0_4571,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5) != X6
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)
| ~ class_Rings_Oring(X1) ),
inference(rename_variables,[],[i_0_2517]) ).
cnf(i_0_4572,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,X1)),X2))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X3),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3409,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518]) ).
cnf(i_0_4573,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(rename_variables,[],[i_0_3534]) ).
cnf(i_0_4574,plain,
( X1 != c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X3,X4)),X5),X6)
| c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5),X1) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5),X6)
| ~ class_Rings_Oring(X2) ),
inference(rename_variables,[],[i_0_2518]) ).
cnf(i_0_4575,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),X3)) = X3,
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_3409,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528]) ).
cnf(i_0_4576,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X2),X4),
inference(rename_variables,[],[i_0_2538]) ).
cnf(i_0_4577,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3) = X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(rename_variables,[],[i_0_2528]) ).
cnf(i_0_4578,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X1),X4)),X2),X3),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529]) ).
cnf(i_0_4579,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X2),X4),
inference(rename_variables,[],[i_0_2538]) ).
cnf(i_0_4580,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)
| X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(rename_variables,[],[i_0_2529]) ).
cnf(i_0_4581,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530]) ).
cnf(i_0_4582,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(rename_variables,[],[i_0_3534]) ).
cnf(i_0_4583,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4) = X6
| ~ class_Rings_Oring(X1) ),
inference(rename_variables,[],[i_0_2530]) ).
cnf(i_0_4584,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531]) ).
cnf(i_0_4585,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(rename_variables,[],[i_0_3534]) ).
cnf(i_0_4586,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| X4 = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)
| ~ class_Rings_Oring(X1) ),
inference(rename_variables,[],[i_0_2531]) ).
cnf(i_0_4587,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X1),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703]) ).
cnf(i_0_4588,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_4589,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_2703]) ).
cnf(i_0_4590,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704]) ).
cnf(i_0_4591,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_3408]) ).
cnf(i_0_4592,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_3409]) ).
cnf(i_0_4593,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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_2704]) ).
cnf(i_0_4594,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_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889]) ).
cnf(i_0_4595,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_2889]) ).
cnf(i_0_4596,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959]) ).
cnf(i_0_4597,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),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_2886]) ).
cnf(i_0_4598,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_2959]) ).
cnf(i_0_4599,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk17_2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966]) ).
cnf(i_0_4600,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_3401]) ).
cnf(i_0_4601,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4602,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk17_2(X2,X1),X2) ),
inference(rename_variables,[],[i_0_2966]) ).
cnf(i_0_4603,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044]) ).
cnf(i_0_4604,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3044]) ).
cnf(i_0_4605,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048]) ).
cnf(i_0_4606,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_3124]) ).
cnf(i_0_4607,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3048]) ).
cnf(i_0_4608,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116]) ).
cnf(i_0_4609,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4610,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_3116]) ).
cnf(i_0_4611,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136]) ).
cnf(i_0_4612,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4613,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X2)) ),
inference(rename_variables,[],[i_0_3136]) ).
cnf(i_0_4614,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244]) ).
cnf(i_0_4615,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4616,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3726]) ).
cnf(i_0_4617,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(rename_variables,[],[i_0_3244]) ).
cnf(i_0_4618,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245]) ).
cnf(i_0_4619,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_3729]) ).
cnf(i_0_4620,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != X3
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3245]) ).
cnf(i_0_4621,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249]) ).
cnf(i_0_4622,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ),
inference(rename_variables,[],[i_0_3249]) ).
cnf(i_0_4623,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250]) ).
cnf(i_0_4624,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
inference(rename_variables,[],[i_0_3407]) ).
cnf(i_0_4625,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_3250]) ).
cnf(i_0_4626,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266]) ).
cnf(i_0_4627,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4628,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3266]) ).
cnf(i_0_4629,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274]) ).
cnf(i_0_4630,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_3715]) ).
cnf(i_0_4631,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3274]) ).
cnf(i_0_4632,plain,
~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281]) ).
cnf(i_0_4633,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3726]) ).
cnf(i_0_4634,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rename_variables,[],[i_0_3143]) ).
cnf(i_0_4635,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3281]) ).
cnf(i_0_4636,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300]) ).
cnf(i_0_4637,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(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(rename_variables,[],[i_0_3300]) ).
cnf(i_0_4638,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311]) ).
cnf(i_0_4639,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4640,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3311]) ).
cnf(i_0_4641,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,v_cs____) != c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,v_cs____),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312]) ).
cnf(i_0_4642,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X2,X3,X1) != c_Polynomial_OpCons(X2,X4,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(rename_variables,[],[i_0_3312]) ).
cnf(i_0_4643,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324]) ).
cnf(i_0_4644,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4645,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3324]) ).
cnf(i_0_4646,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325]) ).
cnf(i_0_4647,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4648,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3325]) ).
cnf(i_0_4649,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1))),X2),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342]) ).
cnf(i_0_4650,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X4,X3)
| X2 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_3342]) ).
cnf(i_0_4651,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1)),X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343]) ).
cnf(i_0_4652,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4)
| X3 = X4
| ~ class_Groups_Ocancel__ab__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_3343]) ).
cnf(i_0_4653,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X2)),X3)) = X1,
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345]) ).
cnf(i_0_4654,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4)
| X3 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_3345]) ).
cnf(i_0_4655,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(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_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361]) ).
cnf(i_0_4656,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_3709]) ).
cnf(i_0_4657,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3361]) ).
cnf(i_0_4658,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380]) ).
cnf(i_0_4659,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3380]) ).
cnf(i_0_4660,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381]) ).
cnf(i_0_4661,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_3381]) ).
cnf(i_0_4662,plain,
X1 = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418]) ).
cnf(i_0_4663,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4664,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = X3 ),
inference(rename_variables,[],[i_0_3418]) ).
cnf(i_0_4665,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(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_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459]) ).
cnf(i_0_4666,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3726]) ).
cnf(i_0_4667,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_3459]) ).
cnf(i_0_4668,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511]) ).
cnf(i_0_4669,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3511]) ).
cnf(i_0_4670,plain,
X1 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512]) ).
cnf(i_0_4671,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3512]) ).
cnf(i_0_4672,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513]) ).
cnf(i_0_4673,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = X1,
inference(rename_variables,[],[i_0_3711]) ).
cnf(i_0_4674,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3513]) ).
cnf(i_0_4675,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(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_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524]) ).
cnf(i_0_4676,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_3524]) ).
cnf(i_0_4677,plain,
~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526]) ).
cnf(i_0_4678,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4679,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(rename_variables,[],[i_0_3526]) ).
cnf(i_0_4680,plain,
~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554]) ).
cnf(i_0_4681,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_3554]) ).
cnf(i_0_4682,plain,
~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555]) ).
cnf(i_0_4683,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_3555]) ).
cnf(i_0_4684,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556]) ).
cnf(i_0_4685,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_3556]) ).
cnf(i_0_4686,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557]) ).
cnf(i_0_4687,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_3557]) ).
cnf(i_0_4688,plain,
c_Polynomial_Osmult(tc_Int_Oint,X1,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585]) ).
cnf(i_0_4689,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4690,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X2,X3,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Oidom(X2) ),
inference(rename_variables,[],[i_0_3585]) ).
cnf(i_0_4691,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586]) ).
cnf(i_0_4692,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4693,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(rename_variables,[],[i_0_3586]) ).
cnf(i_0_4694,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591]) ).
cnf(i_0_4695,plain,
( X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(rename_variables,[],[i_0_3591]) ).
cnf(i_0_4696,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592]) ).
cnf(i_0_4697,plain,
( X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| c_Groups_Oplus__class_Oplus(X2,X3,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(rename_variables,[],[i_0_3592]) ).
cnf(i_0_4698,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644]) ).
cnf(i_0_4699,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_3644]) ).
cnf(i_0_4700,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655]) ).
cnf(i_0_4701,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_3655]) ).
cnf(i_0_4702,plain,
hAPP(c_Polynomial_Opoly(tc_Int_Oint,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))))),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666]) ).
cnf(i_0_4703,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4704,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Opoly(X2,X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(rename_variables,[],[i_0_3666]) ).
cnf(i_0_4705,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749]) ).
cnf(i_0_4706,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) != X3
| c_Groups_Ouminus__class_Ouminus(X1,X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3749]) ).
cnf(i_0_4707,plain,
X1 = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751]) ).
cnf(i_0_4708,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4709,plain,
( X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| X3 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| ~ class_Groups_Ogroup__add(X2) ),
inference(rename_variables,[],[i_0_3751]) ).
cnf(i_0_4710,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752]) ).
cnf(i_0_4711,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X2) ),
inference(rename_variables,[],[i_0_3752]) ).
cnf(i_0_4712,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Int_Oint,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753]) ).
cnf(i_0_4713,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4714,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X2) ),
inference(rename_variables,[],[i_0_3753]) ).
cnf(i_0_4715,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755]) ).
cnf(i_0_4716,plain,
( c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X2)
| c_Groups_Ozero__class_Ozero(X1) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3755]) ).
cnf(i_0_4717,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1)),X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756]) ).
cnf(i_0_4718,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3756]) ).
cnf(i_0_4719,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765]) ).
cnf(i_0_4720,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_4271]) ).
cnf(i_0_4721,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(rename_variables,[],[i_0_3765]) ).
cnf(i_0_4722,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766]) ).
cnf(i_0_4723,plain,
( c_Groups_Ozero__class_Ozero(X1) != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3766]) ).
cnf(i_0_4724,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769]) ).
cnf(i_0_4725,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X1) = X1
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(rename_variables,[],[i_0_3769]) ).
cnf(i_0_4726,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770]) ).
cnf(i_0_4727,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(rename_variables,[],[i_0_3770]) ).
cnf(i_0_4728,plain,
~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1),v_cs____),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204]) ).
cnf(i_0_4729,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X3),X1)
| ~ class_Fields_Ofield(X2) ),
inference(rename_variables,[],[i_0_4204]) ).
cnf(i_0_4730,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047]) ).
cnf(i_0_4731,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4732,plain,
~ c_Orderings_Oord__class_Oless(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,tc_Int_Oint)),X1,X1),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105]) ).
cnf(i_0_4733,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4734,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106]) ).
cnf(i_0_4735,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_4269]) ).
cnf(i_0_4736,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107]) ).
cnf(i_0_4737,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4738,plain,
class_Rings_Oordered__ring(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108]) ).
cnf(i_0_4739,plain,
class_Rings_Ocomm__ring(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109]) ).
cnf(i_0_4740,plain,
class_Rings_Odvd(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110]) ).
cnf(i_0_4741,plain,
class_Rings_Olinordered__semidom(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111]) ).
cnf(i_0_4742,plain,
class_RealVector_Oreal__normed__algebra__1(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3907,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137]) ).
cnf(i_0_4743,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3907,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138]) ).
cnf(i_0_4744,plain,
class_Rings_Olinordered__idom(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3907,i_0_3913,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139]) ).
cnf(i_0_4745,plain,
class_Rings_Olinordered__comm__semiring__strict(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3884,i_0_3907,i_0_3913,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140]) ).
cnf(i_0_4746,plain,
class_Orderings_Oord(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3884,i_0_3907,i_0_3913,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141]) ).
cnf(i_0_4747,plain,
class_Rings_Oordered__comm__semiring(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3884,i_0_3907,i_0_3913,i_0_3918,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142]) ).
cnf(i_0_4748,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143]) ).
cnf(i_0_4749,plain,
class_Groups_Oordered__ab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144]) ).
cnf(i_0_4750,plain,
class_Power_Opower(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145]) ).
cnf(i_0_4751,plain,
class_Groups_Oab__semigroup__mult(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146]) ).
cnf(i_0_4752,plain,
class_Groups_Oordered__comm__monoid__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147]) ).
cnf(i_0_4753,plain,
class_Rings_Oordered__cancel__semiring(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148]) ).
cnf(i_0_4754,plain,
class_Fields_Ofield(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149]) ).
cnf(i_0_4755,plain,
class_Groups_Olinordered__ab__group__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150]) ).
cnf(i_0_4756,plain,
class_Groups_Oab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151]) ).
cnf(i_0_4757,plain,
class_Groups_Ozero(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152]) ).
cnf(i_0_4758,plain,
tc_Int_Oint != tc_Nat_Onat,
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153]) ).
cnf(i_0_4759,plain,
class_Divides_Oring__div(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154]) ).
cnf(i_0_4760,plain,
class_RealVector_Oreal__normed__div__algebra(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157]) ).
cnf(i_0_4761,plain,
class_Orderings_Opreorder(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158]) ).
cnf(i_0_4762,plain,
class_Orderings_Oorder(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159]) ).
cnf(i_0_4763,plain,
tc_RealDef_Oreal != tc_Nat_Onat,
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160]) ).
cnf(i_0_4764,plain,
class_Orderings_Olinorder(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161]) ).
cnf(i_0_4765,plain,
class_Groups_Ocancel__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162]) ).
cnf(i_0_4766,plain,
class_Groups_Ocancel__ab__semigroup__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163]) ).
cnf(i_0_4767,plain,
class_Rings_Oidom(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164]) ).
cnf(i_0_4768,plain,
class_Rings_Omult__zero(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165]) ).
cnf(i_0_4769,plain,
class_Rings_Ono__zero__divisors(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166]) ).
cnf(i_0_4770,plain,
class_Rings_Ozero__neq__one(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167]) ).
cnf(i_0_4771,plain,
class_Rings_Oring__1__no__zero__divisors(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168]) ).
cnf(i_0_4772,plain,
class_Rings_Oring__no__zero__divisors(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169]) ).
cnf(i_0_4773,plain,
class_Int_Oring__char__0(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170]) ).
cnf(i_0_4774,plain,
class_Groups_Omonoid__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171]) ).
cnf(i_0_4775,plain,
class_Groups_Ocancel__comm__monoid__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172]) ).
cnf(i_0_4776,plain,
class_Groups_Oone(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173]) ).
cnf(i_0_4777,plain,
~ c_Rings_Odvd__class_Odvd(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174]) ).
cnf(i_0_4778,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4779,plain,
~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175]) ).
cnf(i_0_4780,plain,
~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176]) ).
cnf(i_0_4781,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(rename_variables,[],[i_0_3535]) ).
cnf(i_0_4782,plain,
class_RealVector_Oreal__normed__algebra(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177]) ).
cnf(i_0_4783,plain,
class_Rings_Ocomm__ring__1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178]) ).
cnf(i_0_4784,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X1)),X2)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470]) ).
cnf(i_0_4785,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4786,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2470]) ).
cnf(i_0_4787,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)),X3)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478]) ).
cnf(i_0_4788,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2478]) ).
cnf(i_0_4789,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713]) ).
cnf(i_0_4790,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rename_variables,[],[i_0_3226]) ).
cnf(i_0_4791,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_2713]) ).
cnf(i_0_4792,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_Oone__class_Oone(tc_Nat_Onat),X1),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715]) ).
cnf(i_0_4793,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_2715]) ).
cnf(i_0_4794,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(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796]) ).
cnf(i_0_4795,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_2796]) ).
cnf(i_0_4796,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_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899]) ).
cnf(i_0_4797,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4798,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_2899]) ).
cnf(i_0_4799,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977]) ).
cnf(i_0_4800,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_2977]) ).
cnf(i_0_4801,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979]) ).
cnf(i_0_4802,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4803,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1) ),
inference(rename_variables,[],[i_0_2979]) ).
cnf(i_0_4804,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980]) ).
cnf(i_0_4805,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_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X2) ),
inference(rename_variables,[],[i_0_2980]) ).
cnf(i_0_4806,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),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_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990]) ).
cnf(i_0_4807,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4808,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_2990]) ).
cnf(i_0_4809,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_3739,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058]) ).
cnf(i_0_4810,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3739]) ).
cnf(i_0_4811,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(rename_variables,[],[i_0_3058]) ).
cnf(i_0_4812,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059]) ).
cnf(i_0_4813,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3739]) ).
cnf(i_0_4814,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
inference(rename_variables,[],[i_0_3059]) ).
cnf(i_0_4815,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_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067]) ).
cnf(i_0_4816,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_3712]) ).
cnf(i_0_4817,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4818,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_3067]) ).
cnf(i_0_4819,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117]) ).
cnf(i_0_4820,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4821,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_3117]) ).
cnf(i_0_4822,plain,
~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230]) ).
cnf(i_0_4823,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4824,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_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3230]) ).
cnf(i_0_4825,plain,
~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248]) ).
cnf(i_0_4826,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3724]) ).
cnf(i_0_4827,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
inference(rename_variables,[],[i_0_3248]) ).
cnf(i_0_4828,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260]) ).
cnf(i_0_4829,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4830,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3260]) ).
cnf(i_0_4831,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264]) ).
cnf(i_0_4832,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3264]) ).
cnf(i_0_4833,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280]) ).
cnf(i_0_4834,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3280]) ).
cnf(i_0_4835,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308]) ).
cnf(i_0_4836,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4837,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3308]) ).
cnf(i_0_4838,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310]) ).
cnf(i_0_4839,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3310]) ).
cnf(i_0_4840,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315]) ).
cnf(i_0_4841,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3315]) ).
cnf(i_0_4842,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316]) ).
cnf(i_0_4843,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3316]) ).
cnf(i_0_4844,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321]) ).
cnf(i_0_4845,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4846,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3321]) ).
cnf(i_0_4847,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323]) ).
cnf(i_0_4848,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rename_variables,[],[i_0_3323]) ).
cnf(i_0_4849,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk37_2(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346]) ).
cnf(i_0_4850,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_3346]) ).
cnf(i_0_4851,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347]) ).
cnf(i_0_4852,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_3347]) ).
cnf(i_0_4853,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354]) ).
cnf(i_0_4854,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_3354]) ).
cnf(i_0_4855,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369]) ).
cnf(i_0_4856,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| X2 != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rename_variables,[],[i_0_3369]) ).
cnf(i_0_4857,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444]) ).
cnf(i_0_4858,plain,
( X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
| ~ class_Rings_Odvd(X2)
| c_Rings_Odvd__class_Odvd(X2,X3,X1) ),
inference(rename_variables,[],[i_0_3444]) ).
cnf(i_0_4859,plain,
class_Rings_Oring(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112]) ).
cnf(i_0_4860,plain,
class_Groups_Omonoid__mult(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113]) ).
cnf(i_0_4861,plain,
class_Rings_Osemiring(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114]) ).
cnf(i_0_4862,plain,
class_Rings_Olinordered__semiring__1__strict(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3866,i_0_3870,i_0_3873,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115]) ).
cnf(i_0_4863,plain,
class_Rings_Olinordered__semiring__1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116]) ).
cnf(i_0_4864,plain,
hBOOL(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_fequal(X1,X1)))))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120]) ).
cnf(i_0_4865,plain,
class_Rings_Osemiring__0(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121]) ).
cnf(i_0_4866,plain,
class_Rings_Olinordered__ring__strict(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122]) ).
cnf(i_0_4867,plain,
class_Rings_Ocomm__semiring__1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123]) ).
cnf(i_0_4868,plain,
class_Rings_Olinordered__ring(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124]) ).
cnf(i_0_4869,plain,
class_Rings_Ocomm__semiring__0(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125]) ).
cnf(i_0_4870,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126]) ).
cnf(i_0_4871,plain,
class_Divides_Osemiring__div(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127]) ).
cnf(i_0_4872,plain,
class_Rings_Oring__1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3884,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128]) ).
cnf(i_0_4873,plain,
class_Rings_Olinordered__semiring__strict(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129]) ).
cnf(i_0_4874,plain,
class_RealVector_Oreal__normed__vector(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130]) ).
cnf(i_0_4875,plain,
class_Rings_Oordered__semiring(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131]) ).
cnf(i_0_4876,plain,
class_Groups_Ocomm__monoid__mult(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132]) ).
cnf(i_0_4877,plain,
class_Rings_Olinordered__semiring(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133]) ).
cnf(i_0_4878,plain,
tc_Complex_Ocomplex != tc_Nat_Onat,
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134]) ).
cnf(i_0_4879,plain,
class_Groups_Ocomm__monoid__add(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135]) ).
cnf(i_0_4880,plain,
class_Rings_Ocomm__semiring(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136]) ).
cnf(i_0_4881,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774]) ).
cnf(i_0_4882,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_2774]) ).
cnf(i_0_4883,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775]) ).
cnf(i_0_4884,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_3176]) ).
cnf(i_0_4885,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_4239]) ).
cnf(i_0_4886,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_2775]) ).
cnf(i_0_4887,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_Oone__class_Oone(tc_Nat_Onat),X2)),X3),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776]) ).
cnf(i_0_4888,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_3408]) ).
cnf(i_0_4889,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_2776]) ).
cnf(i_0_4890,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942]) ).
cnf(i_0_4891,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4892,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4266]) ).
cnf(i_0_4893,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_2942]) ).
cnf(i_0_4894,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943]) ).
cnf(i_0_4895,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4896,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4266]) ).
cnf(i_0_4897,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_2943]) ).
cnf(i_0_4898,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944]) ).
cnf(i_0_4899,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4900,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_2944]) ).
cnf(i_0_4901,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945]) ).
cnf(i_0_4902,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4903,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,X4,X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_2945]) ).
cnf(i_0_4904,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,esk37_2(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216]) ).
cnf(i_0_4905,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_4269]) ).
cnf(i_0_4906,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_3216]) ).
cnf(i_0_4907,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283]) ).
cnf(i_0_4908,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_3283]) ).
cnf(i_0_4909,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335]) ).
cnf(i_0_4910,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
inference(rename_variables,[],[i_0_3407]) ).
cnf(i_0_4911,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3726]) ).
cnf(i_0_4912,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| X3 = X2
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_3335]) ).
cnf(i_0_4913,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),X1),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_3409,i_0_4567,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493]) ).
cnf(i_0_4914,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_3176]) ).
cnf(i_0_4915,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_3493]) ).
cnf(i_0_4916,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_3409,i_0_4567,i_0_4592,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587]) ).
cnf(i_0_4917,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_3409]) ).
cnf(i_0_4918,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_3408]) ).
cnf(i_0_4919,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_2587]) ).
cnf(i_0_4920,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588]) ).
cnf(i_0_4921,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_4922,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_3409]) ).
cnf(i_0_4923,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_2588]) ).
cnf(i_0_4924,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670]) ).
cnf(i_0_4925,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4926,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4927,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
inference(rename_variables,[],[i_0_2670]) ).
cnf(i_0_4928,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891]) ).
cnf(i_0_4929,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4930,plain,
( ~ 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))
| 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) ),
inference(rename_variables,[],[i_0_2891]) ).
cnf(i_0_4931,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892]) ).
cnf(i_0_4932,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3740]) ).
cnf(i_0_4933,plain,
( ~ 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))
| 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) ),
inference(rename_variables,[],[i_0_2892]) ).
cnf(i_0_4934,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893]) ).
cnf(i_0_4935,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4936,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_2893]) ).
cnf(i_0_4937,plain,
~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1)),v_cs____),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973]) ).
cnf(i_0_4938,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4939,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X3),X4)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X3,X4)
| ~ class_Fields_Ofield(X2) ),
inference(rename_variables,[],[i_0_2973]) ).
cnf(i_0_4940,plain,
~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_cs____)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975]) ).
cnf(i_0_4941,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4942,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X3,c_Polynomial_Osmult(X2,X1,X4))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X3,X4)
| ~ class_Fields_Ofield(X2) ),
inference(rename_variables,[],[i_0_2975]) ).
cnf(i_0_4943,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)) = X1,
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978]) ).
cnf(i_0_4944,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
inference(rename_variables,[],[i_0_3405]) ).
cnf(i_0_4945,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_4946,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_3408]) ).
cnf(i_0_4947,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 = X3 ),
inference(rename_variables,[],[i_0_2978]) ).
cnf(i_0_4948,plain,
~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),X1),v_cs____),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088]) ).
cnf(i_0_4949,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4950,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X4),X1)
| ~ class_Fields_Ofield(X2) ),
inference(rename_variables,[],[i_0_3088]) ).
cnf(i_0_4951,plain,
c_Polynomial_Opos__poly(tc_Int_Oint,c_Polynomial_OpCons(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180]) ).
cnf(i_0_4952,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4953,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4954,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X3,X1))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rename_variables,[],[i_0_3180]) ).
cnf(i_0_4955,plain,
c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Polynomial_Osmult(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),X2),c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287]) ).
cnf(i_0_4956,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4957,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X4),X1)
| ~ class_Fields_Ofield(X2) ),
inference(rename_variables,[],[i_0_3287]) ).
cnf(i_0_4958,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530]) ).
cnf(i_0_4959,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4960,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1) ),
inference(rename_variables,[],[i_0_3530]) ).
cnf(i_0_4961,plain,
c_Polynomial_OpCons(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544]) ).
cnf(i_0_4962,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3773]) ).
cnf(i_0_4963,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_OpCons(X2,X3,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ozero(X2) ),
inference(rename_variables,[],[i_0_3544]) ).
cnf(i_0_4964,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214]) ).
cnf(i_0_4965,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4966,plain,
( ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),X2)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(rename_variables,[],[i_0_4214]) ).
cnf(i_0_4967,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1,
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216]) ).
cnf(i_0_4968,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4969,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rename_variables,[],[i_0_3385]) ).
cnf(i_0_4970,plain,
( ~ class_Divides_Osemiring__div(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2) = X3
| ~ c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) ),
inference(rename_variables,[],[i_0_4216]) ).
cnf(i_0_4971,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))))),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773]) ).
cnf(i_0_4972,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_2773]) ).
cnf(i_0_4973,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_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).
cnf(i_0_4974,plain,
( ~ 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))
| 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) ),
inference(rename_variables,[],[i_0_2890]) ).
cnf(i_0_4975,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(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894]) ).
cnf(i_0_4976,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_2894]) ).
cnf(i_0_4977,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914]) ).
cnf(i_0_4978,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4979,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(rename_variables,[],[i_0_2914]) ).
cnf(i_0_4980,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941]) ).
cnf(i_0_4981,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_4982,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4266]) ).
cnf(i_0_4983,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_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_2941]) ).
cnf(i_0_4984,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082]) ).
cnf(i_0_4985,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_3409]) ).
cnf(i_0_4986,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3726]) ).
cnf(i_0_4987,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_3082]) ).
cnf(i_0_4988,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083]) ).
cnf(i_0_4989,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(rename_variables,[],[i_0_4271]) ).
cnf(i_0_4990,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3742]) ).
cnf(i_0_4991,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_3083]) ).
cnf(i_0_4992,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))),v_cs____),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678]) ).
cnf(i_0_4993,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(rename_variables,[],[i_0_3534]) ).
cnf(i_0_4994,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4995,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != c_Groups_Oplus__class_Oplus(X1,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X6))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X4 = X6
| X2 != X5 ),
inference(rename_variables,[],[i_0_2678]) ).
cnf(i_0_4996,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201]) ).
cnf(i_0_4997,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_4998,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rename_variables,[],[i_0_3385]) ).
cnf(i_0_4999,plain,
( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
| X4 = c_Groups_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X2,X1,X4) != X3
| ~ c_Rings_Odvd__class_Odvd(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X2) ),
inference(rename_variables,[],[i_0_3201]) ).
cnf(i_0_5000,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1,
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204]) ).
cnf(i_0_5001,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),
inference(rename_variables,[],[i_0_3574]) ).
cnf(i_0_5002,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_5003,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rename_variables,[],[i_0_3385]) ).
cnf(i_0_5004,plain,
( X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
| X4 = c_Groups_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X2,X1,X4) = X3
| ~ c_Rings_Odvd__class_Odvd(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X2) ),
inference(rename_variables,[],[i_0_3204]) ).
cnf(i_0_5005,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111]) ).
cnf(i_0_5006,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),
inference(rename_variables,[],[i_0_3633]) ).
cnf(i_0_5007,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_3111]) ).
cnf(i_0_5008,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255]) ).
cnf(i_0_5009,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_5010,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2) ),
inference(rename_variables,[],[i_0_4255]) ).
cnf(i_0_5011,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735]) ).
cnf(i_0_5012,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_3745]) ).
cnf(i_0_5013,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_5014,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3739]) ).
cnf(i_0_5015,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rename_variables,[],[i_0_3385]) ).
cnf(i_0_5016,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,X4) = c_Divides_Odiv__class_Odiv(X1,X5,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X2)
| ~ class_Divides_Osemiring__div(X1) ),
inference(rename_variables,[],[i_0_2735]) ).
cnf(i_0_5017,plain,
esk37_2(X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723]) ).
cnf(i_0_5018,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3723]) ).
cnf(i_0_5019,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952]) ).
cnf(i_0_5020,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
inference(rename_variables,[],[i_0_2952]) ).
cnf(i_0_5021,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,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955]) ).
cnf(i_0_5022,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_2955]) ).
cnf(i_0_5023,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1)),X2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998]) ).
cnf(i_0_5024,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(rename_variables,[],[i_0_2998]) ).
cnf(i_0_5025,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035]) ).
cnf(i_0_5026,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3035]) ).
cnf(i_0_5027,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049]) ).
cnf(i_0_5028,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3049]) ).
cnf(i_0_5029,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057]) ).
cnf(i_0_5030,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3057]) ).
cnf(i_0_5031,plain,
esk17_2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119]) ).
cnf(i_0_5032,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_Oone__class_Oone(tc_Nat_Onat)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3119]) ).
cnf(i_0_5033,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162]) ).
cnf(i_0_5034,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3162]) ).
cnf(i_0_5035,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165]) ).
cnf(i_0_5036,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3165]) ).
cnf(i_0_5037,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183]) ).
cnf(i_0_5038,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3183]) ).
cnf(i_0_5039,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255]) ).
cnf(i_0_5040,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3255]) ).
cnf(i_0_5041,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_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).
cnf(i_0_5042,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(rename_variables,[],[i_0_3445]) ).
cnf(i_0_5043,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527]) ).
cnf(i_0_5044,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(rename_variables,[],[i_0_3527]) ).
cnf(i_0_5045,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541]) ).
cnf(i_0_5046,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) ),
inference(rename_variables,[],[i_0_3541]) ).
cnf(i_0_5047,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560]) ).
cnf(i_0_5048,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3560]) ).
cnf(i_0_5049,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561]) ).
cnf(i_0_5050,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3561]) ).
cnf(i_0_5051,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566]) ).
cnf(i_0_5052,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_3566]) ).
cnf(i_0_5053,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580]) ).
cnf(i_0_5054,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3580]) ).
cnf(i_0_5055,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703]) ).
cnf(i_0_5056,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_3703]) ).
cnf(i_0_5057,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_cs____,
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_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).
cnf(i_0_5058,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,esk37_2(X1,X2),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251]) ).
cnf(i_0_5059,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X1) ),
inference(rename_variables,[],[i_0_3251]) ).
cnf(i_0_5060,plain,
( ~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X1,X2) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442]) ).
cnf(i_0_5061,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3442]) ).
cnf(i_0_5062,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507]) ).
cnf(i_0_5063,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_3507]) ).
cnf(i_0_5064,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509]) ).
cnf(i_0_5065,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_3509]) ).
cnf(i_0_5066,plain,
( ~ class_Rings_Olinordered__ring__strict(tc_HOL_Obool)
| c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1))) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607]) ).
cnf(i_0_5067,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_5068,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(rename_variables,[],[i_0_2607]) ).
cnf(i_0_5069,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2),X2) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793]) ).
cnf(i_0_5070,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_5071,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4) ),
inference(rename_variables,[],[i_0_2793]) ).
cnf(i_0_5072,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026]) ).
cnf(i_0_5073,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(rename_variables,[],[i_0_4215]) ).
cnf(i_0_5074,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3026]) ).
cnf(i_0_5075,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027]) ).
cnf(i_0_5076,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_5077,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3027]) ).
cnf(i_0_5078,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239]) ).
cnf(i_0_5079,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_5080,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(rename_variables,[],[i_0_3239]) ).
cnf(i_0_5081,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X2)),X3)) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279]) ).
cnf(i_0_5082,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3279]) ).
cnf(i_0_5083,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X2),X2))) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379]) ).
cnf(i_0_5084,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3727]) ).
cnf(i_0_5085,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3379]) ).
cnf(i_0_5086,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X5))),X3)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468]) ).
cnf(i_0_5087,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2468]) ).
cnf(i_0_5088,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X4))),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,X3)),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480]) ).
cnf(i_0_5089,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2480]) ).
cnf(i_0_5090,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),X2,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))))) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984]) ).
cnf(i_0_5091,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rename_variables,[],[i_0_2984]) ).
cnf(i_0_5092,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Polynomial_Osmult(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),X2),c_Polynomial_Osmult(tc_RealDef_Oreal,X3,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)))))) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984,i_0_3113]) ).
cnf(i_0_5093,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rename_variables,[],[i_0_3113]) ).
cnf(i_0_5094,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984,i_0_3113,i_0_3114]) ).
cnf(i_0_5095,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(rename_variables,[],[i_0_3114]) ).
cnf(i_0_5096,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984,i_0_3113,i_0_3114,i_0_3115]) ).
cnf(i_0_5097,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(rename_variables,[],[i_0_3115]) ).
cnf(i_0_5098,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_5079,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984,i_0_3113,i_0_3114,i_0_3115,i_0_3141]) ).
cnf(i_0_5099,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_5100,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3141]) ).
cnf(i_0_5101,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1))) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_5079,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984,i_0_3113,i_0_3114,i_0_3115,i_0_3141,i_0_3227]) ).
cnf(i_0_5102,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Groups_Oordered__ab__group__add(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_3227]) ).
cnf(i_0_5103,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X2)) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_5079,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3949,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984,i_0_3113,i_0_3114,i_0_3115,i_0_3141,i_0_3227,i_0_2875]) ).
cnf(i_0_5104,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(rename_variables,[],[i_0_2875]) ).
cnf(i_0_5105,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))),X2) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_5079,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3949,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984,i_0_3113,i_0_3114,i_0_3115,i_0_3141,i_0_3227,i_0_2875,i_0_3438]) ).
cnf(i_0_5106,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(rename_variables,[],[i_0_3438]) ).
cnf(i_0_5107,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk37_2(X2,X3)) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_5079,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3949,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984,i_0_3113,i_0_3114,i_0_3115,i_0_3141,i_0_3227,i_0_2875,i_0_3438,i_0_3529]) ).
cnf(i_0_5108,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(rename_variables,[],[i_0_3529]) ).
cnf(i_0_5109,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_5079,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3949,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984,i_0_3113,i_0_3114,i_0_3115,i_0_3141,i_0_3227,i_0_2875,i_0_3438,i_0_3529,i_0_3098]) ).
cnf(i_0_5110,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(rename_variables,[],[i_0_3098]) ).
cnf(i_0_5111,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_HOL_Obool),X1),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(esk37_2(X2,X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(scs_inference,[],[i_0_4304,i_0_4252,i_0_3696,i_0_4251,i_0_4253,i_0_4266,i_0_4352,i_0_4378,i_0_4460,i_0_4892,i_0_4896,i_0_4269,i_0_4735,i_0_3740,i_0_4341,i_0_4490,i_0_4493,i_0_4502,i_0_4512,i_0_4515,i_0_4542,i_0_4555,i_0_4609,i_0_4612,i_0_4627,i_0_4639,i_0_4891,i_0_4899,i_0_4925,i_0_4929,i_0_3741,i_0_4326,i_0_4329,i_0_4332,i_0_4509,i_0_4563,i_0_4588,i_0_4921,i_0_3742,i_0_4315,i_0_4318,i_0_4372,i_0_4388,i_0_4505,i_0_4508,i_0_4518,i_0_4558,i_0_4644,i_0_4902,i_0_4935,i_0_4271,i_0_4570,i_0_4720,i_0_4289,i_0_4237,i_0_4391,i_0_4785,i_0_4802,i_0_4820,i_0_4829,i_0_4836,i_0_4845,i_0_4895,i_0_4926,i_0_4953,i_0_4978,i_0_4981,i_0_5070,i_0_5079,i_0_4270,i_0_3534,i_0_4538,i_0_4573,i_0_4582,i_0_4585,i_0_3535,i_0_4452,i_0_3780,i_0_3407,i_0_4624,i_0_3408,i_0_4335,i_0_4338,i_0_4346,i_0_4349,i_0_4591,i_0_4888,i_0_4918,i_0_3409,i_0_4567,i_0_4592,i_0_4917,i_0_4922,i_0_3726,i_0_4564,i_0_4616,i_0_4633,i_0_4666,i_0_4911,i_0_3729,i_0_3633,i_0_4525,i_0_3915,i_0_3706,i_0_3773,i_0_4397,i_0_4536,i_0_4615,i_0_4689,i_0_4692,i_0_4703,i_0_4708,i_0_4713,i_0_4733,i_0_4778,i_0_4949,i_0_4952,i_0_4956,i_0_3745,i_0_3143,i_0_4363,i_0_4366,i_0_4540,i_0_3604,i_0_4323,i_0_3405,i_0_4394,i_0_3711,i_0_3712,i_0_4816,i_0_3715,i_0_3448,i_0_3268,i_0_3709,i_0_3574,i_0_3840,i_0_3710,i_0_2538,i_0_4576,i_0_3622,i_0_4550,i_0_4737,i_0_4797,i_0_4807,i_0_4817,i_0_3739,i_0_4810,i_0_4813,i_0_4215,i_0_4239,i_0_4885,i_0_3175,i_0_4381,i_0_4467,i_0_4470,i_0_3176,i_0_4355,i_0_4545,i_0_4884,i_0_3623,i_0_3724,i_0_3727,i_0_3849,i_0_3853,i_0_3854,i_0_3855,i_0_3856,i_0_3857,i_0_3858,i_0_3859,i_0_3862,i_0_3866,i_0_3870,i_0_3873,i_0_3876,i_0_3878,i_0_3881,i_0_3884,i_0_3887,i_0_3890,i_0_3892,i_0_3896,i_0_3900,i_0_3901,i_0_3902,i_0_3903,i_0_3907,i_0_3909,i_0_3913,i_0_3918,i_0_3921,i_0_3924,i_0_3927,i_0_3931,i_0_3935,i_0_3939,i_0_3940,i_0_3942,i_0_3946,i_0_3948,i_0_3949,i_0_3950,i_0_3951,i_0_3952,i_0_3953,i_0_3954,i_0_3955,i_0_3956,i_0_3957,i_0_3959,i_0_3963,i_0_3968,i_0_3969,i_0_3970,i_0_3972,i_0_3974,i_0_3975,i_0_3976,i_0_3978,i_0_3980,i_0_3982,i_0_3986,i_0_3988,i_0_3990,i_0_3991,i_0_3994,i_0_3996,i_0_3997,i_0_3998,i_0_3999,i_0_4002,i_0_4003,i_0_4004,i_0_4005,i_0_4006,i_0_4007,i_0_4008,i_0_4011,i_0_4014,i_0_4015,i_0_4016,i_0_4020,i_0_4022,i_0_4023,i_0_4024,i_0_4025,i_0_4027,i_0_4028,i_0_4029,i_0_4030,i_0_4034,i_0_4037,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_3705,i_0_3845,i_0_3385,i_0_4969,i_0_4998,i_0_5003,i_0_3401,i_0_4442,i_0_2886,i_0_4455,i_0_2887,i_0_3226,i_0_4449,i_0_4790,i_0_3589,i_0_4409,i_0_4601,i_0_4647,i_0_4663,i_0_4678,i_0_4731,i_0_4938,i_0_4941,i_0_4959,i_0_4965,i_0_4968,i_0_4994,i_0_4997,i_0_5002,i_0_5009,i_0_5013,i_0_5067,i_0_3124,i_0_3569,i_0_4360,i_0_4375,i_0_3078,i_0_3357,i_0_3416,i_0_3475,i_0_2826,i_0_2852,i_0_2854,i_0_2940,i_0_2964,i_0_3053,i_0_3055,i_0_3056,i_0_3073,i_0_3074,i_0_3167,i_0_3171,i_0_3172,i_0_3181,i_0_3194,i_0_3196,i_0_3277,i_0_3356,i_0_3384,i_0_3393,i_0_3394,i_0_3410,i_0_3411,i_0_3417,i_0_3446,i_0_3455,i_0_3466,i_0_3468,i_0_3473,i_0_3528,i_0_3577,i_0_3600,i_0_3607,i_0_3611,i_0_3612,i_0_3613,i_0_3695,i_0_3704,i_0_3722,i_0_4182,i_0_4183,i_0_4186,i_0_4187,i_0_4222,i_0_4046,i_0_4067,i_0_4068,i_0_2721,i_0_2853,i_0_2949,i_0_2965,i_0_2997,i_0_3060,i_0_3070,i_0_3152,i_0_3166,i_0_3177,i_0_3187,i_0_3190,i_0_3192,i_0_3256,i_0_3276,i_0_3388,i_0_3443,i_0_3587,i_0_3694,i_0_4217,i_0_4218,i_0_2465,i_0_2469,i_0_2717,i_0_2719,i_0_3003,i_0_3118,i_0_3121,i_0_3137,i_0_3262,i_0_3309,i_0_3322,i_0_3350,i_0_3355,i_0_3382,i_0_3440,i_0_3685,i_0_3686,i_0_3687,i_0_4117,i_0_4118,i_0_4119,i_0_2471,i_0_2472,i_0_2473,i_0_2474,i_0_2475,i_0_2479,i_0_2481,i_0_2482,i_0_2483,i_0_2485,i_0_2517,i_0_2518,i_0_2528,i_0_2529,i_0_2530,i_0_2531,i_0_2703,i_0_2704,i_0_2889,i_0_2959,i_0_2966,i_0_3044,i_0_3048,i_0_3116,i_0_3136,i_0_3244,i_0_3245,i_0_3249,i_0_3250,i_0_3266,i_0_3274,i_0_3281,i_0_3300,i_0_3311,i_0_3312,i_0_3324,i_0_3325,i_0_3342,i_0_3343,i_0_3345,i_0_3361,i_0_3380,i_0_3381,i_0_3418,i_0_3459,i_0_3511,i_0_3512,i_0_3513,i_0_3524,i_0_3526,i_0_3554,i_0_3555,i_0_3556,i_0_3557,i_0_3585,i_0_3586,i_0_3591,i_0_3592,i_0_3644,i_0_3655,i_0_3666,i_0_3749,i_0_3751,i_0_3752,i_0_3753,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3769,i_0_3770,i_0_4204,i_0_4047,i_0_4105,i_0_4106,i_0_4107,i_0_4108,i_0_4109,i_0_4110,i_0_4111,i_0_4137,i_0_4138,i_0_4139,i_0_4140,i_0_4141,i_0_4142,i_0_4143,i_0_4144,i_0_4145,i_0_4146,i_0_4147,i_0_4148,i_0_4149,i_0_4150,i_0_4151,i_0_4152,i_0_4153,i_0_4154,i_0_4157,i_0_4158,i_0_4159,i_0_4160,i_0_4161,i_0_4162,i_0_4163,i_0_4164,i_0_4165,i_0_4166,i_0_4167,i_0_4168,i_0_4169,i_0_4170,i_0_4171,i_0_4172,i_0_4173,i_0_4174,i_0_4175,i_0_4176,i_0_4177,i_0_4178,i_0_2470,i_0_2478,i_0_2713,i_0_2715,i_0_2796,i_0_2899,i_0_2977,i_0_2979,i_0_2980,i_0_2990,i_0_3058,i_0_3059,i_0_3067,i_0_3117,i_0_3230,i_0_3248,i_0_3260,i_0_3264,i_0_3280,i_0_3308,i_0_3310,i_0_3315,i_0_3316,i_0_3321,i_0_3323,i_0_3346,i_0_3347,i_0_3354,i_0_3369,i_0_3444,i_0_4112,i_0_4113,i_0_4114,i_0_4115,i_0_4116,i_0_4120,i_0_4121,i_0_4122,i_0_4123,i_0_4124,i_0_4125,i_0_4126,i_0_4127,i_0_4128,i_0_4129,i_0_4130,i_0_4131,i_0_4132,i_0_4133,i_0_4134,i_0_4135,i_0_4136,i_0_2774,i_0_2775,i_0_2776,i_0_2942,i_0_2943,i_0_2944,i_0_2945,i_0_3216,i_0_3283,i_0_3335,i_0_3493,i_0_2587,i_0_2588,i_0_2670,i_0_2891,i_0_2892,i_0_2893,i_0_2973,i_0_2975,i_0_2978,i_0_3088,i_0_3180,i_0_3287,i_0_3530,i_0_3544,i_0_4214,i_0_4216,i_0_2773,i_0_2890,i_0_2894,i_0_2914,i_0_2941,i_0_3082,i_0_3083,i_0_2678,i_0_3201,i_0_3204,i_0_3111,i_0_4255,i_0_2735,i_0_3723,i_0_2952,i_0_2955,i_0_2998,i_0_3035,i_0_3049,i_0_3057,i_0_3119,i_0_3162,i_0_3165,i_0_3183,i_0_3255,i_0_3445,i_0_3527,i_0_3541,i_0_3560,i_0_3561,i_0_3566,i_0_3580,i_0_3703,i_0_4061,i_0_3251,i_0_3442,i_0_3507,i_0_3509,i_0_2607,i_0_2793,i_0_3026,i_0_3027,i_0_3239,i_0_3279,i_0_3379,i_0_2468,i_0_2480,i_0_2984,i_0_3113,i_0_3114,i_0_3115,i_0_3141,i_0_3227,i_0_2875,i_0_3438,i_0_3529,i_0_3098,i_0_3138]) ).
cnf(i_0_5112,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2) ),
inference(rename_variables,[],[i_0_3138]) ).
cnf(i_0_5113,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_5114,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,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_2887]) ).
cnf(i_0_5115,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_5116,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_5117,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3739]) ).
cnf(i_0_5118,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_3401]) ).
cnf(i_0_5119,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3741]) ).
cnf(i_0_5120,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3590]) ).
cnf(i_0_5121,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4237]) ).
cnf(i_0_5122,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_5123,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rename_variables,[],[i_0_3143]) ).
cnf(i_0_5124,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3739]) ).
cnf(i_0_5125,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_5126,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3739]) ).
cnf(i_0_5127,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_5128,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_3408]) ).
cnf(i_0_5129,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_5130,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_3175]) ).
cnf(i_0_5131,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(rename_variables,[],[i_0_3535]) ).
cnf(i_0_5132,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(rename_variables,[],[i_0_3535]) ).
cnf(i_0_5133,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),
inference(rename_variables,[],[i_0_4252]) ).
cnf(i_0_5134,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_5135,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3739]) ).
cnf(i_0_5136,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3590]) ).
cnf(i_0_5137,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3590]) ).
cnf(i_0_5139,plain,
$false,
inference(scs_inference,[],[i_0_4313,i_0_4311,i_0_4312]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW232+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n009.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 06:27:56 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.72/5.79 % Version : CSE_E---1.7
% 1.72/5.79 % Problem : theBenchmark.p
% 1.72/5.79 % SZS status Theorem for theBenchmark.p
% 1.72/5.79 % SZS output start CNFRefutation
% See solution above
% 46.36/28.69 % Total time : 5.451s
%------------------------------------------------------------------------------