%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW225+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 : n020.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 05:30:35 PM UTC 2026
% Result : Theorem 6.22s 5.80s
% Output : CNFRefutation 6.42s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1474)
% Comments :
%------------------------------------------------------------------------------
fof(fact_div__if,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__if) ).
fof(fact_div__geq,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__geq) ).
fof(fact_Suc__nat__number__of__add,axiom,
! [X6,X49] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X6) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X49)),X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of__add) ).
fof(fact_le__SucE,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Nat_OSuc(X6))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> X7 = c_Nat_OSuc(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_not__less__eq__eq,axiom,
! [X19,X18] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X19,X18] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_less__SucE,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Nat_OSuc(X6))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_less__antisym,axiom,
! [X7,X6] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(X7))
=> X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X18))
<=> X19 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X6),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_nat__number__of__diff__1,axiom,
! [X49] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__diff__1) ).
fof(fact_nat__number__of__add__1,axiom,
! [X49] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__add__1) ).
fof(fact_nat__1__add__number__of,axiom,
! [X49] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__number__of) ).
fof(fact_Suc__nat__number__of,axiom,
! [X49] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).
fof(fact_lift__Suc__mono__le,axiom,
! [X32,X19,X2,X5] :
( class_Orderings_Oorder(X5)
=> ( ! [X31] : c_Orderings_Oord__class_Oless__eq(X5,hAPP(X2,X31),hAPP(X2,c_Nat_OSuc(X31)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X32)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(X2,X19),hAPP(X2,X32)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lift__Suc__mono__le) ).
fof(fact_Suc__eq__plus1,axiom,
! [X6] : c_Nat_OSuc(X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_realpow__two__diff,axiom,
! [X23,X4,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X23),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X23)),c_Groups_Oplus__class_Oplus(X5,X4,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X21)),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X21)),X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X21)),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X21)),X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(fact_reals__Archimedean4,axiom,
! [X4,X23] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> ? [X31] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X31)),X23),X4)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X31))),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean4) ).
fof(fact_cis__real__of__nat__Suc__mult,axiom,
! [X13,X6] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X6))),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X13)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)),X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__real__of__nat__Suc__mult) ).
fof(fact_cis__rcis__eq,axiom,
! [X13] : c_Complex_Ocis(X13) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__rcis__eq) ).
fof(fact_lemma__NBseq__def2,axiom,
! [X34,X25] :
( class_RealVector_Oreal__normed__vector(X25)
=> ( ? [X62] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& ! [X31] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X25,hAPP(X34,X31)),X62) )
<=> ? [X63] :
! [X31] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X25,hAPP(X34,X31)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X63))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def2) ).
fof(fact_lemma__NBseq__def,axiom,
! [X34,X25] :
( class_RealVector_Oreal__normed__vector(X25)
=> ( ? [X62] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& ! [X31] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X25,hAPP(X34,X31)),X62) )
<=> ? [X63] :
! [X31] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X25,hAPP(X34,X31)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X63))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def) ).
fof(fact_Bseq__iff1a,axiom,
! [X34,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X34)
<=> ? [X63] :
! [X31] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X34,X31)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X63))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__iff1a) ).
fof(fact_Bseq__iff,axiom,
! [X34,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X34)
<=> ? [X63] :
! [X31] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X34,X31)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X63))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__iff) ).
fof(fact_power__le__imp__le__base,axiom,
! [X12,X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Nat_OSuc(X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),c_Nat_OSuc(X6)))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_split__div_H,axiom,
! [X19,X18,X42] :
( hBOOL(hAPP(X42,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X18,X19)))
<=> ( ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X96] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X96),X18)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),c_Nat_OSuc(X96)))
& hBOOL(hAPP(X42,X96)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div_H) ).
fof(fact_lemma__realpow__diff,axiom,
! [X23,X6,X87,X5] :
( class_Groups_Omonoid__mult(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X87,X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X23),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X6),X87)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X23),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X87))),X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__realpow__diff) ).
fof(fact_split__div__lemma,axiom,
! [X18,X95,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
=> ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X95),X18)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),c_Nat_OSuc(X95))) )
<=> X95 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X18,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div__lemma) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [X23,X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X23)),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [X19,X10,X90,X91,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X91,X90),X10),c_Nat_OSuc(X19)) = hAPP(hAPP(X90,X10),hAPP(hAPP(c_Power_Opower_Opower(X5,X91,X90),X10),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(fact_Suc__mult__cancel1,axiom,
! [X19,X18,X21] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X21)),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X21)),X19)
<=> X18 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_one__less__mult,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7)
=> 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),X7),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
fof(fact_one__le__mult__iff,axiom,
! [X19,X18] :
( 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),X18),X19))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_mono__SucI2,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( ! [X31] : c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,c_Nat_OSuc(X31)),hAPP(X34,X31))
=> c_SEQ_Omonoseq(X5,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__SucI2) ).
fof(fact_monoseq__Suc,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Omonoseq(X5,X34)
<=> ( ! [X31] : c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,X31),hAPP(X34,c_Nat_OSuc(X31)))
| ! [X31] : c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,c_Nat_OSuc(X31)),hAPP(X34,X31)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monoseq__Suc) ).
fof(fact_mono__SucI1,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( ! [X31] : c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,X31),hAPP(X34,c_Nat_OSuc(X31)))
=> c_SEQ_Omonoseq(X5,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__SucI1) ).
fof(fact_incseq__SucI,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( ! [X31] : c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,X31),hAPP(X34,c_Nat_OSuc(X31)))
=> c_SEQ_Oincseq(X5,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incseq__SucI) ).
fof(fact_nat__number__of__mult__left,axiom,
! [X15,X68,X49] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)),X15)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)),X15)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X68))),X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).
fof(fact_diff__Suc__diff__eq2,axiom,
! [X7,X16,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X16)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X15)),X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X16),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [X7,X16,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X16)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X15))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X15),c_Nat_OSuc(X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(fact_power__inject__base,axiom,
! [X12,X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Nat_OSuc(X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),c_Nat_OSuc(X6))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> X13 = X12 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).
fof(fact_int__power__div__base,axiom,
! [X15,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X15)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15),X7),X15) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,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,
! [X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4 = 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,
! [X8,X10,X42] :
( hBOOL(hAPP(X42,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X8)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X8)
& ~ hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X44] :
( X10 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X44)
& ~ hBOOL(hAPP(X42,X44)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_n__less__n__mult__m,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_n__less__m__mult__n,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_Suc__diff__diff,axiom,
! [X15,X6,X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X7),X6),c_Nat_OSuc(X15)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
fof(fact_of__nat__aux_Osimps_I2_J,axiom,
! [X36,X19,X37,X5] :
( class_Rings_Osemiring__1(X5)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X37,c_Nat_OSuc(X19),X36) = c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X37,X19,hAPP(X37,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
fof(fact_divmod__int__rel__div__eq,axiom,
! [X92,X23,X93,X94] :
( X94 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X93),X23),X92)
=> ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X93)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X92)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X92,X93) ) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X93)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X93,X92)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X92,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
=> ( X93 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X94,X93) = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).
fof(fact_le__div__geq,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__div__geq) ).
fof(fact_power__Suc__less__one,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Nat_OSuc(X6)),c_Groups_Oone__class_Oone(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_realpow__Suc__le__self,axiom,
! [X6,X54,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X54)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X54,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X54),c_Nat_OSuc(X6)),X54) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
fof(fact_subseq__Suc__iff,axiom,
! [X2] :
( c_SEQ_Osubseq(X2)
<=> ! [X31] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X31),hAPP(X2,c_Nat_OSuc(X31))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__Suc__iff) ).
fof(fact_nat__number__of__add__left,axiom,
! [X15,X68,X49] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68),X15)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68),X15) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X68))
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68),X15)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),X15) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X68))
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68),X15)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X68)),X15) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__add__left) ).
fof(fact_Suc__diff__number__of,axiom,
! [X7,X49] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X49)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X7),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(X49))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__number__of) ).
fof(fact_pred__def,axiom,
! [X15] : c_Int_Opred(X15) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X15,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__def) ).
fof(fact_zless__iff__Suc__zadd,axiom,
! [X56,X51] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,X56)
<=> ? [X31] : X56 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X31))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).
fof(fact_succ__def,axiom,
! [X15] : c_Int_Osucc(X15) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__def) ).
fof(fact_nat__one__le__power,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)
=> 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),X17),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
fof(fact_power__gt1,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X13)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Nat_OSuc(X6))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
fof(fact_Suc__less__SucD,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X7),c_Nat_OSuc(X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__less__eq,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X18),c_Nat_OSuc(X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__le__mono,axiom,
! [X18,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_Suc__pred,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).
fof(fact_diff__Suc__less,axiom,
! [X17,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Nat_OSuc(X17)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_ex__least__nat__less,axiom,
! [X19,X42] :
( ~ hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X42,X19))
=> ? [X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X19)
& ! [X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X22)
=> ~ hBOOL(hAPP(X42,X48)) )
& hBOOL(hAPP(X42,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,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,
! [X6,X7] :
( ( X7 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6) = X6 )
& ( X7 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(fact_split__zdiv,axiom,
! [X21,X19,X42] :
( hBOOL(hAPP(X42,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X19,X21)))
<=> ( ( X21 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ! [X48] :
( ? [X38] :
( 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,X21)
& X19 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X48),X38) )
=> hBOOL(hAPP(X42,X48)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X48] :
( ? [X38] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X38)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& X19 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X48),X38) )
=> hBOOL(hAPP(X42,X48)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zdiv) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
! [X81,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X81)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X81)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(fact_power__Suc2,axiom,
! [X6,X13,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Nat_OSuc(X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
fof(fact_reals__Archimedean6a,axiom,
! [X54] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X54)
=> ? [X31] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X31),X54)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X54,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X31))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6a) ).
fof(fact_mult__Suc,axiom,
! [X6,X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X7)),X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
fof(fact_Suc__diff__le,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X7),X6) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
fof(fact_neg__number__of__pred__iff__0,axiom,
! [X53] :
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X53)))
<=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X53) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__pred__iff__0) ).
fof(fact_less__add__Suc1,axiom,
! [X7,X17] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X7,X17] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_le__Suc__eq,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Nat_OSuc(X19))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19)
| X18 = c_Nat_OSuc(X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_Suc__mono,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X7),c_Nat_OSuc(X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_natfloor__add__number__of,axiom,
! [X4,X6] :
( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X6))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X6))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add__number__of) ).
fof(fact_natceiling__add__number__of,axiom,
! [X4,X6] :
( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X6))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X6))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add__number__of) ).
fof(fact_le__number__of__eq__not__less,axiom,
! [X51,X53,X5] :
( ( class_Int_Onumber(X5)
& class_Orderings_Olinorder(X5) )
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Int_Onumber__class_Onumber__of(X5,X53),c_Int_Onumber__class_Onumber__of(X5,X51))
<=> ~ c_Orderings_Oord__class_Oless(X5,c_Int_Onumber__class_Onumber__of(X5,X51),c_Int_Onumber__class_Onumber__of(X5,X53)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).
fof(fact_expand__Suc,axiom,
! [X49] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49))
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__Suc) ).
fof(fact_DeMoivre,axiom,
! [X6,X13] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X13)),X6) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DeMoivre) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X19))
<=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X38] :
( X18 = c_Nat_OSuc(X38)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_le__less__Suc__eq,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X18))
<=> X19 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_power__Suc__0,axiom,
! [X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X6) = 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,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X15)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X17),X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_abs__add__one__not__less__self,axiom,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
fof(fact_diff__Suc__Suc,axiom,
! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X7),c_Nat_OSuc(X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
fof(fact_add__Suc__shift,axiom,
! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X7),X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Nat_OSuc(X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_diff__Suc__eq__diff__pred,axiom,
! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Nat_OSuc(X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
fof(fact_power__Suc,axiom,
! [X6,X13,X5] :
( class_Power_Opower(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Nat_OSuc(X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
! [X81,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X81)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X81)) ),
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,
! [X81,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X81)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X81)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(fact_add__Suc,axiom,
! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X7),X6) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__right,axiom,
! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Nat_OSuc(X6)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_le__natfloor__eq__number__of,axiom,
! [X24,X19] :
( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X19))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X19),c_RComplete_Onatfloor(X24))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X19),X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__number__of) ).
fof(fact_natceiling__le__eq__number__of,axiom,
! [X24,X19] :
( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X19))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X24),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X19)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__number__of) ).
fof(fact_add__nat__number__of,axiom,
! [X68,X49] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X68)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nat__number__of) ).
fof(fact_less__Suc__eq,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19)
| X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__lessD,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X7),X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_less__eq__Suc__le,axiom,
! [X18,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__le__eq,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X18),X19)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_Suc__le__lessD,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X7),X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_le__iff__pred__less,axiom,
! [X30,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X30)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X21),X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__pred__less) ).
fof(fact_Suc__leD,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X7),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_less__Suc__eq__le,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_real__of__nat__Suc__gt__zero,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
fof(fact_less__iff__Suc__add,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19)
<=> ? [X22] : X19 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_Suc__lessI,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> ( c_Nat_OSuc(X7) != X6
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X7),X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_add__leE,axiom,
! [X6,X15,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X15),X6)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_mult__Suc__right,axiom,
! [X6,X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),c_Nat_OSuc(X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_one__is__add,axiom,
! [X19,X18] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X19)
<=> ( ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X18 = 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_one__is__add) ).
fof(fact_add__is__1,axiom,
! [X19,X18] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X19) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X18 = 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_add__is__1) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X5,X25] :
( class_Orderings_Oord(X25)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X5,X25),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X25),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X25),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_mult__eq__1__iff,axiom,
! [X19,X18] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X19) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X18 = c_Nat_OSuc(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_mult__eq__1__iff) ).
fof(fact_less__Suc0,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_mult__nat__number__of,axiom,
! [X68,X49] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X68)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).
fof(fact_diff__less__Suc,axiom,
! [X6,X7] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),c_Nat_OSuc(X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_not__square__less__zero,axiom,
! [X13,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X13),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_cis__mult,axiom,
! [X12,X13] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X13)),c_Complex_Ocis(X12)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__mult) ).
fof(fact_le__nat__number__of,axiom,
! [X67,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X53),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X67))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X67)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,c_Int_OPls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__nat__number__of) ).
fof(fact_Suc__diff__1,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
fof(fact_Suc__pred_H,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> X6 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
fof(fact_Suc__leI,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X7),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_less__SucI,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Nat_OSuc(X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_le__imp__less__Suc,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Nat_OSuc(X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_le__SucI,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Nat_OSuc(X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_not__add__less1,axiom,
! [X16,X17] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X16),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X17,X16] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X17),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_not__real__square__gt__zero,axiom,
! [X24] :
( ~ 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),X24),X24))
<=> X24 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(fact_of__nat__Suc,axiom,
! [X7,X5] :
( class_Rings_Osemiring__1(X5)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Nat_OSuc(X7)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__Suc) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [X18,X24] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X18) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X24 = 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_number__of__succ,axiom,
! [X15,X5] :
( class_Int_Onumber__ring(X5)
=> c_Int_Onumber__class_Onumber__of(X5,c_Int_Osucc(X15)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Int_Onumber__class_Onumber__of(X5,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__succ) ).
fof(fact_eq__nat__number__of,axiom,
! [X67,X53] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X53) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X67)
<=> ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X53))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X67),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X53))
=> ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X67))
=> c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X53) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X67))
=> X53 = X67 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).
fof(fact_real__of__nat__Suc,axiom,
! [X6] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X6)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
fof(fact_int__Suc,axiom,
! [X7] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X7)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc) ).
fof(fact_add__diff__inverse,axiom,
! [X6,X7] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_less__le__not__le,axiom,
! [X27,X24,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
& ~ c_Orderings_Oord__class_Oless__eq(X5,X27,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_power__0__Suc,axiom,
! [X6,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Osemiring__0(X5) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),c_Nat_OSuc(X6)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
fof(fact_of__nat__number__of__lemma,axiom,
! [X49,X5] :
( class_Int_Onumber__ring(X5)
=> ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(X5,X49) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__number__of__lemma) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> X24 = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X13,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X13)
=> ~ c_Orderings_Oord__class_Oless(X5,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> ( c_Orderings_Oord__class_Oless(X5,X27,X24)
| X24 = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_leD,axiom,
! [X4,X23,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,X4)
=> ~ c_Orderings_Oord__class_Oless(X5,X4,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__less,axiom,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> c_Orderings_Oord__class_Oless__eq(X5,X27,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
<=> c_Orderings_Oord__class_Oless(X5,X27,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_order__less__asym,axiom,
! [X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> ~ c_Orderings_Oord__class_Oless(X5,X23,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X12,X13,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ~ c_Orderings_Oord__class_Oless(X5,X12,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> ~ c_Orderings_Oord__class_Oless(X5,X23,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> ~ c_Orderings_Oord__class_Oless(X5,X23,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_nat_Oinject,axiom,
! [X28,X29] :
( c_Nat_OSuc(X29) = c_Nat_OSuc(X28)
<=> X29 = X28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_Suc__inject,axiom,
! [X23,X4] :
( c_Nat_OSuc(X4) = c_Nat_OSuc(X23)
=> X4 = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(fact_div__1,axiom,
! [X7] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__1) ).
fof(fact_diff__Suc__1,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
fof(fact_succ__pred,axiom,
! [X4] : c_Int_Osucc(c_Int_Opred(X4)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__pred) ).
fof(fact_zero__less__Suc,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_lessI,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_of__nat__less__0__iff,axiom,
! [X7,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X7),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).
fof(fact_gr0__conv__Suc,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
<=> ? [X35] : X19 = c_Nat_OSuc(X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_tsub__def,axiom,
! [X4,X23] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X4)
=> c_Nat__Transfer_Otsub(X4,X23) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,X23) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X4)
=> c_Nat__Transfer_Otsub(X4,X23) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__def) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X24,X27)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
<=> X24 = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_abs__not__less__zero,axiom,
! [X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,X13),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
fof(fact_int__less__0__conv,axiom,
! [X15] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__less__0__conv) ).
fof(fact_not__real__of__nat__less__zero,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
fof(fact_norm__not__less__zero,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X23,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X4 != X23
=> ( ~ c_Orderings_Oord__class_Oless(X5,X4,X23)
=> c_Orderings_Oord__class_Oless(X5,X23,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__cases,axiom,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X4,X23)
=> ( X4 != X23
=> c_Orderings_Oord__class_Oless(X5,X23,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( X4 != X23
=> ( ~ c_Orderings_Oord__class_Oless(X5,X4,X23)
=> c_Orderings_Oord__class_Oless(X5,X23,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X24,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X24)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> X24 = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_not__leE,axiom,
! [X4,X23,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X23,X4)
=> c_Orderings_Oord__class_Oless(X5,X4,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X4,X23)
=> c_Orderings_Oord__class_Oless__eq(X5,X23,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_linorder__le__cases,axiom,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X4,X23)
=> c_Orderings_Oord__class_Oless__eq(X5,X23,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_not__one__less__zero,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_not__one__le__zero,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X6] : c_Nat_OSuc(X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_linorder__neqE__nat,axiom,
! [X23,X4] :
( X4 != X23
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X23)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_of__nat__number__of__eq,axiom,
! [X49,X5] :
( class_Int_Onumber__ring(X5)
=> ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Ozero__class_Ozero(X5) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(X5,X49) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__number__of__eq) ).
fof(fact_not__neg__eq__ge__0,axiom,
! [X24] :
( ~ c_Nat__Numeral_Oneg(X24)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__eq__ge__0) ).
fof(fact_order__less__irrefl,axiom,
! [X4,X5] :
( class_Orderings_Opreorder(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,X4,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_Suc__neq__Zero,axiom,
! [X7] : c_Nat_OSuc(X7) != 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,
! [X46] : c_Nat_OSuc(X46) != 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,
! [X7] : c_Nat_OSuc(X7) != 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,
! [X7] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X45] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X45),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__not__Suc,axiom,
! [X7] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_Suc__n__not__n,axiom,
! [X6] : c_Nat_OSuc(X6) != X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X6] : X6 != c_Nat_OSuc(X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_less__nat__zero__code,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_not__less0,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__zeroE,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_int__nat__number__of,axiom,
! [X49] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__nat__number__of) ).
fof(fact_real__of__nat__number__of,axiom,
! [X49] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X49) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__number__of) ).
fof(fact_less__irrefl__nat,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_not__neg__int,axiom,
! [X6] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__int) ).
fof(fact_lemmaCauchy,axiom,
! [X34,X69,X5,X25] :
( ( class_RealVector_Oreal__normed__vector(X25)
& class_Orderings_Oord(X5) )
=> ( ! [X31] :
( c_Orderings_Oord__class_Oless__eq(X5,X69,X31)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X25,c_Groups_Ominus__class_Ominus(X25,hAPP(X34,X69),hAPP(X34,X31))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
=> ! [X31] :
( c_Orderings_Oord__class_Oless__eq(X5,X69,X31)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X25,hAPP(X34,X31)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X25,hAPP(X34,X69)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemmaCauchy) ).
fof(fact_decr__lemma,axiom,
! [X26,X4,X14] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,X26)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X14)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__lemma) ).
fof(fact_incr__lemma,axiom,
! [X4,X26,X14] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,X26)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__lemma) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X5,X25] :
( class_Orderings_Oord(X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X25),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X25,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [X12,X13,X23,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X13)),c_Groups_Ominus__class_Ominus(X5,X23,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X13)),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),c_Groups_Ominus__class_Ominus(X5,X23,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_less__add__iff1,axiom,
! [X41,X8,X9,X79,X10,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X79),X9),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X79),X41))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X10,X8)),X79),X9),X41) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(fact_le__add__iff1,axiom,
! [X41,X8,X9,X79,X10,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X79),X9),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X79),X41))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X10,X8)),X79),X9),X41) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
fof(fact_less__add__iff2,axiom,
! [X41,X8,X9,X79,X10,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X79),X9),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X79),X41))
<=> c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X8,X10)),X79),X41)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(fact_le__add__iff2,axiom,
! [X41,X8,X9,X79,X10,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X79),X9),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X79),X41))
<=> c_Orderings_Oord__class_Oless__eq(X5,X9,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X8,X10)),X79),X41)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(fact_nat__less__add__iff1,axiom,
! [X19,X18,X84,X36,X43] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43,X36)
=> ( 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),X36),X84),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X84),X19))
<=> 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,X36,X43)),X84),X18),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_nat__le__add__iff1,axiom,
! [X19,X18,X84,X36,X43] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43,X36)
=> ( 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),X36),X84),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X84),X19))
<=> 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,X36,X43)),X84),X18),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__less__add__iff2,axiom,
! [X19,X18,X84,X43,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X43)
=> ( 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),X36),X84),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X84),X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,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,X43,X36)),X84),X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
fof(fact_nat__le__add__iff2,axiom,
! [X19,X18,X84,X43,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X43)
=> ( 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),X36),X84),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X84),X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,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,X43,X36)),X84),X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_abs__diff__triangle__ineq,axiom,
! [X14,X11,X12,X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),c_Groups_Oplus__class_Oplus(X5,X11,X14))),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X13,X11)),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X12,X14)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).
fof(fact_reduce__poly__simple,axiom,
! [X6,X12] :
( X12 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X89] : 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),X12),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X89),X6)))),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,
! [X14,X11,X12,X13,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),c_Groups_Oplus__class_Oplus(X5,X11,X14))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X13,X11)),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X12,X14)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).
fof(fact_nat__diff__add__eq1,axiom,
! [X6,X7,X80,X17,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X17)
=> 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),X17),X80),X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X80),X6)) = 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,X17,X16)),X80),X7),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_nat__diff__add__eq2,axiom,
! [X6,X7,X80,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X16)
=> 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),X17),X80),X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X80),X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,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,X16,X17)),X80),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_decr__mult__lemma,axiom,
! [X21,X42,X41] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X41)
=> ( ! [X3] :
( hBOOL(hAPP(X42,X3))
=> hBOOL(hAPP(X42,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X41))) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ! [X3] :
( hBOOL(hAPP(X42,X3))
=> hBOOL(hAPP(X42,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X41)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).
fof(fact_incr__mult__lemma,axiom,
! [X21,X42,X41] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X41)
=> ( ! [X3] :
( hBOOL(hAPP(X42,X3))
=> hBOOL(hAPP(X42,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X41))) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ! [X3] :
( hBOOL(hAPP(X42,X3))
=> hBOOL(hAPP(X42,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X41)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [X82,X83,X71,X54,X81,X12] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X81),X54) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X83),X82)
=> ( 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),X71),X83),X82),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X12)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X82)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X71)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X71,X12)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X83,X81) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [X82,X83,X71,X54,X81,X12] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X81),X54) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X71),X83),X82)
=> ( 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),X71),X83),X82))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X82,X71)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X71)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X71,X12)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,X83) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_zdiff__int__split,axiom,
! [X27,X24,X42] :
( hBOOL(hAPP(X42,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X27))))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X24)
=> hBOOL(hAPP(X42,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27)))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X27)
=> hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__int__split) ).
fof(fact_mult_Ononneg__bounded,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X62] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& ! [X85,X86] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X85),X86)),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(X5,X85)),c_RealVector_Onorm__class_Onorm(X5,X86))),X62)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ononneg__bounded) ).
fof(fact_mult_Opos__bounded,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X62] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& ! [X85,X86] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X85),X86)),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(X5,X85)),c_RealVector_Onorm__class_Onorm(X5,X86))),X62)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).
fof(fact_unique__quotient__lemma,axiom,
! [X54,X81,X82,X83,X12] :
( 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),X12),X83),X82),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X81),X54))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X82)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X82,X12)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X12)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X83,X81) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [X54,X81,X82,X83,X12] :
( 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),X12),X83),X82),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X81),X54))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X54)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X82)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,X83) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_nat__eq__add__iff1,axiom,
! [X19,X18,X84,X36,X43] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43,X36)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X84),X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X84),X19)
<=> 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,X36,X43)),X84),X18) = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__eq__add__iff2,axiom,
! [X19,X18,X84,X43,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X43)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X84),X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X84),X19)
<=> X18 = 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,X43,X36)),X84),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_eq__add__iff1,axiom,
! [X41,X8,X9,X79,X10,X5] :
( class_Rings_Oring(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X79),X9) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X79),X41)
<=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X10,X8)),X79),X9) = X41 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [X41,X8,X9,X79,X10,X5] :
( class_Rings_Oring(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X79),X9) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X79),X41)
<=> X9 = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X8,X10)),X79),X41) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
! [X6,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_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)),X4),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,X4,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
fof(fact_unimodular__reduce__norm,axiom,
! [X26] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X26) = 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,X26,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,X26,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,X26,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,X26,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,
! [X12,X13,X23,X4,X5] :
( class_Rings_Oring(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ominus__class_Ominus(X5,X23,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X13)),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_combine__common__factor,axiom,
! [X11,X12,X47,X13,X5] :
( class_Rings_Osemiring(X5)
=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X47),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X47),X11)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X13,X12)),X47),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_convex__bound__lt,axiom,
! [X49,X80,X23,X13,X4,X5] :
( class_Rings_Olinordered__semiring__1__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X13)
=> ( c_Orderings_Oord__class_Oless(X5,X23,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X80)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X49)
=> ( c_Groups_Oplus__class_Oplus(X5,X80,X49) = c_Groups_Oone__class_Oone(X5)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X80),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X49),X23)),X13) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_convex__bound__le,axiom,
! [X49,X80,X23,X13,X4,X5] :
( class_Rings_Olinordered__semiring__1(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X80)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X49)
=> ( c_Groups_Oplus__class_Oplus(X5,X80,X49) = c_Groups_Oone__class_Oone(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X80),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X49),X23)),X13) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(fact_BseqI,axiom,
! [X34,X70,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X70)
=> ( ! [X31] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X34,X31)),X70)
=> c_SEQ_OBseq(X5,X34) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_BseqI) ).
fof(fact_Bseq__def,axiom,
! [X34,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X34)
<=> ? [X62] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& ! [X31] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X34,X31)),X62) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__def) ).
fof(fact_left__add__mult__distrib,axiom,
! [X15,X16,X80,X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X80),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X80),X15)) = 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,X17,X16)),X80),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X27,X24,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X27)))
<=> ( X24 != c_Groups_Ozero__class_Ozero(X5)
| X27 != c_Groups_Ozero__class_Ozero(X5) ) ) ),
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,
! [X75,X76,X77,X78,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),X77)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X76),X75)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X76),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),X77)),X75)) ),
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,
! [X27,X24,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X27)),c_Groups_Ozero__class_Ozero(X5))
<=> ( X24 = c_Groups_Ozero__class_Ozero(X5)
& X27 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_realpow__minus__mult,axiom,
! [X4,X6,X5] :
( class_Groups_Omonoid__mult(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
fof(fact_lemma__interval,axiom,
! [X12,X4,X13] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X4)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,X12)
=> ? [X44] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X44)
& ! [X55] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4,X55)),X44)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X55)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X55,X12) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__interval) ).
fof(fact_crossproduct__noteq,axiom,
! [X41,X9,X8,X10,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( ( X10 != X8
& X9 != X41 )
<=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X41)) != c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X41),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X56,X24,X27,X51,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X51),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X56)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X51),X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X27))
<=> ( X51 = X24
| X27 = X56 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_abs__diff__less__iff,axiom,
! [X52,X10,X24,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X24,X10)),X52)
<=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ominus__class_Ominus(X5,X10,X52),X24)
& c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Oplus__class_Oplus(X5,X10,X52)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).
fof(fact_mult__number__of__left,axiom,
! [X26,X33,X49,X5] :
( class_Int_Onumber__ring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X5,X49)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X5,X33)),X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X33))),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).
fof(fact_q__neg__lemma,axiom,
! [X82,X83,X71] :
( 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),X71),X83),X82),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),X82)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X71)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X83,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,
! [X82,X83,X71] :
( 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),X71),X83),X82))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X82,X71)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X71)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X83) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_split__div,axiom,
! [X21,X19,X42] :
( hBOOL(hAPP(X42,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X19,X21)))
<=> ( ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( X21 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [X48,X38] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X21)
=> ( X19 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X48),X38)
=> hBOOL(hAPP(X42,X48)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div) ).
fof(fact_abs__triangle__ineq3,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oabs__class_Oabs(X5,X13),c_Groups_Oabs__class_Oabs(X5,X12))),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X13,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).
fof(fact_norm__triangle__ineq3,axiom,
! [X12,X13,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X13),c_RealVector_Onorm__class_Onorm(X5,X12))),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X13,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X75,X76,X77,X78,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),X77)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X76),X75)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),X76)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X77),X75)) ),
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,
! [X75,X76,X77,X78,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),X77)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X76),X75)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X77),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X76),X75))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_right__diff__distrib__number__of,axiom,
! [X11,X12,X49,X25] :
( ( class_Int_Onumber(X25)
& class_Rings_Oring(X25) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),c_Int_Onumber__class_Onumber__of(X25,X49)),c_Groups_Ominus__class_Ominus(X25,X12,X11)) = c_Groups_Ominus__class_Ominus(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),c_Int_Onumber__class_Onumber__of(X25,X49)),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),c_Int_Onumber__class_Onumber__of(X25,X49)),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).
fof(fact_right__distrib__number__of,axiom,
! [X11,X12,X49,X25] :
( ( class_Int_Onumber(X25)
& class_Rings_Osemiring(X25) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),c_Int_Onumber__class_Onumber__of(X25,X49)),c_Groups_Oplus__class_Oplus(X25,X12,X11)) = c_Groups_Oplus__class_Oplus(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),c_Int_Onumber__class_Onumber__of(X25,X49)),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),c_Int_Onumber__class_Onumber__of(X25,X49)),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).
fof(fact_complex__mod__triangle__ineq2,axiom,
! [X13,X12] : 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,X12,X13)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X12)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [X26,X33] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X33),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X33,X26)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X26))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(fact_nat__diff__split,axiom,
! [X8,X10,X42] :
( hBOOL(hAPP(X42,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X8)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X8)
=> hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X44] :
( X10 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X44)
=> hBOOL(hAPP(X42,X44)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(fact_abs__mult__less,axiom,
! [X14,X12,X11,X13,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,X13),X11)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,X12),X14)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X13)),c_Groups_Oabs__class_Oabs(X5,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).
fof(fact_left__diff__distrib__number__of,axiom,
! [X49,X12,X13,X25] :
( ( class_Int_Onumber(X25)
& class_Rings_Oring(X25) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),c_Groups_Ominus__class_Ominus(X25,X13,X12)),c_Int_Onumber__class_Onumber__of(X25,X49)) = c_Groups_Ominus__class_Ominus(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X13),c_Int_Onumber__class_Onumber__of(X25,X49)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X12),c_Int_Onumber__class_Onumber__of(X25,X49))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).
fof(fact_left__distrib__number__of,axiom,
! [X49,X12,X13,X25] :
( ( class_Int_Onumber(X25)
& class_Rings_Osemiring(X25) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),c_Groups_Oplus__class_Oplus(X25,X13,X12)),c_Int_Onumber__class_Onumber__of(X25,X49)) = c_Groups_Oplus__class_Oplus(X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X13),c_Int_Onumber__class_Onumber__of(X25,X49)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X12),c_Int_Onumber__class_Onumber__of(X25,X49))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).
fof(fact_fz_I2_J,axiom,
! [X64] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X64)
=> ? [X63] :
! [X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X63,X31)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X31)),v_z____)),X64) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fz_I2_J) ).
fof(fact_power__Suc__less,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_zmult__zless__mono2__lemma,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X16)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15)),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15)),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).
fof(fact_odd__less__0,axiom,
! [X56] :
( 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),X56),X56),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X56,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,
! [X40,X23,X54,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),X54)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X23),X40)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X54,X40)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__add__less) ).
fof(fact_mult__eq__if,axiom,
! [X6,X7] :
( ( X7 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X7 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(fact_less__diff__iff,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X19)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X21))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(fact_le__diff__iff,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X21))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(fact_mult__strict__mono,axiom,
! [X14,X11,X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless(X5,X11,X14)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X14)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_mult__strict__mono_H,axiom,
! [X14,X11,X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless(X5,X11,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X14)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__le__less__imp__less,axiom,
! [X14,X11,X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless(X5,X11,X14)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X14)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__less__le__imp__less,axiom,
! [X14,X11,X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X11,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X14)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__mono_H,axiom,
! [X14,X11,X12,X13,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X11,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X14)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__mono,axiom,
! [X14,X11,X12,X13,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X11,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X14)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(fact_norm__mult__less,axiom,
! [X40,X23,X54,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),X54)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X23),X40)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X54),X40)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).
fof(fact_power__mult__distrib,axiom,
! [X6,X12,X13,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X81,X23,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X23)),X81) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X81)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X23),X81)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_ath,axiom,
! [X47,X4,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,X4)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,X47))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4,X7)),X47) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ath) ).
fof(fact_sum__squares__ge__zero,axiom,
! [X23,X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_real__squared__diff__one__factored,axiom,
! [X4,X5] :
( class_Rings_Oring__1(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4),c_Groups_Oone__class_Oone(X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oone__class_Oone(X5))),c_Groups_Ominus__class_Ominus(X5,X4,c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(fact_power__less__power__Suc,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X13)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_mult__right__less__imp__less,axiom,
! [X12,X11,X13,X5] :
( class_Rings_Olinordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [X12,X11,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_power__less__imp__less__base,axiom,
! [X12,X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X6))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_mult__left__less__imp__less,axiom,
! [X12,X13,X11,X5] :
( class_Rings_Olinordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [X12,X13,X11,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X8,X10,X9,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X9)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X8))
<=> c_Orderings_Oord__class_Oless(X5,X10,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__right__le__imp__le,axiom,
! [X12,X11,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11))
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [X12,X13,X11,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12))
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [X8,X10,X9,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X8))
<=> c_Orderings_Oord__class_Oless__eq(X5,X10,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X8,X10,X9,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X8))
<=> c_Orderings_Oord__class_Oless(X5,X8,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [X8,X10,X9,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X8))
<=> c_Orderings_Oord__class_Oless__eq(X5,X8,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X65] :
~ ! [X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X31)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X31)),v_z____)),v_d____) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096,axiom,
? [X63] :
! [X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X63,X31)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X31)),v_z____)),v_d____) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096) ).
fof(fact_N1,axiom,
! [X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,X31)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X31)),v_z____)),v_d____) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_N1) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X27,X24,X8,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X8)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X8),X24),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X8),X27))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [X6,X7,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__increasing__iff,axiom,
! [X27,X24,X8,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X8)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X8),X24),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X8),X27))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [X6,X7,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_natceiling__eq,axiom,
! [X4,X6] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6),X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__eq) ).
fof(fact_zadd__int__left,axiom,
! [X26,X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6),X26)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)),X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int__left) ).
fof(fact_le__mult__natfloor,axiom,
! [X12,X13] :
( 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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X13)),c_RComplete_Onatfloor(X12)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
fof(fact_Deriv_Oadd__diff__add,axiom,
! [X14,X12,X11,X13,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),c_Groups_Oplus__class_Oplus(X5,X12,X14)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ominus__class_Ominus(X5,X13,X12),c_Groups_Ominus__class_Ominus(X5,X11,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X14,X11,X12,X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),c_Groups_Oplus__class_Oplus(X5,X11,X14)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),c_Groups_Oplus__class_Oplus(X5,X12,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_power__strict__decreasing,axiom,
! [X13,X88,X6,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X88)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X88),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_power__decreasing,axiom,
! [X13,X88,X6,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X88)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X88),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(fact_div__mult__self2,axiom,
! [X11,X13,X12,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X12 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,c_Groups_Oplus__class_Oplus(X5,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11)),X12) = c_Groups_Oplus__class_Oplus(X5,X11,c_Divides_Odiv__class_Odiv(X5,X13,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2) ).
fof(fact_div__mult__self1,axiom,
! [X11,X13,X12,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X12 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,c_Groups_Oplus__class_Oplus(X5,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12)),X12) = c_Groups_Oplus__class_Oplus(X5,X11,c_Divides_Odiv__class_Odiv(X5,X13,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1) ).
fof(fact_power__strict__mono,axiom,
! [X6,X12,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X6)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(fact_nonzero__power__divide,axiom,
! [X6,X13,X12,X5] :
( class_Fields_Ofield(X5)
=> ( X12 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Rings_Oinverse__class_Odivide(X5,X13,X12)),X6) = c_Rings_Oinverse__class_Odivide(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X8,X10,X9,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X8))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X9)
& c_Orderings_Oord__class_Oless(X5,X10,X8) )
| ( c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless(X5,X8,X10) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X8,X9,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X9))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X9)
& c_Orderings_Oord__class_Oless(X5,X10,X8) )
| ( c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless(X5,X8,X10) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_mult__left_Ononneg__bounded,axiom,
! [X23,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X62] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X62)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ononneg__bounded) ).
fof(fact_mult__left_Opos__bounded,axiom,
! [X23,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X62] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X62)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).
fof(fact_norm__mult__ineq,axiom,
! [X23,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)),c_RealVector_Onorm__class_Onorm(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
fof(fact_mult__right_Ononneg__bounded,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X62] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X62)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ononneg__bounded) ).
fof(fact_mult__right_Opos__bounded,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X62] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X3)),X62)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).
fof(fact_add__number__of__diff1,axiom,
! [X11,X33,X49,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Int_Onumber__class_Onumber__of(X5,X49),c_Groups_Ominus__class_Ominus(X5,c_Int_Onumber__class_Onumber__of(X5,X33),X11)) = c_Groups_Ominus__class_Ominus(X5,c_Int_Onumber__class_Onumber__of(X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X33)),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).
fof(fact_add__number__of__left,axiom,
! [X26,X33,X49,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Int_Onumber__class_Onumber__of(X5,X49),c_Groups_Oplus__class_Oplus(X5,c_Int_Onumber__class_Onumber__of(X5,X33),X26)) = c_Groups_Oplus__class_Oplus(X5,c_Int_Onumber__class_Onumber__of(X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X33)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X12,X7,X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X7)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X13,X12)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_mult_Odiff__left,axiom,
! [X12,X73,X13,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X13,X73)),X12) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X73),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
fof(fact_mult__left_Odiff,axiom,
! [X74,X23,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X23)),X74) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X74),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X74)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X11,X12,X13,X5] :
( class_Rings_Ocomm__semiring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X13,X12)),X11) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_mult__left_Oadd,axiom,
! [X74,X23,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X4,X23)),X74) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X74),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X74)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_mult_Oadd__left,axiom,
! [X12,X73,X13,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X13,X73)),X12) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X73),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X11,X12,X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X13,X12)),X11) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_real__of__nat__div4,axiom,
! [X4,X6] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X6,X4)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__div4) ).
fof(fact_zdiv__mono2,axiom,
! [X12,X71,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X71)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X71,X12)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X71)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
fof(fact_zdiv__mono2__neg,axiom,
! [X12,X71,X13] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X71)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X71,X12)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X71),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X81,X87,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X87)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X81)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X87,X81)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X6,X7,X13,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X7)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X76,X77,X78,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),X77)),X76) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),X76)),X77) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_abs__triangle__ineq2,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oabs__class_Oabs(X5,X13),c_Groups_Oabs__class_Oabs(X5,X12)),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X13,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).
fof(fact_abs__triangle__ineq2__sym,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,c_Groups_Oabs__class_Oabs(X5,X13),c_Groups_Oabs__class_Oabs(X5,X12)),c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X12,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
fof(fact_abs__triangle__ineq4,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X13,X12)),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oabs__class_Oabs(X5,X13),c_Groups_Oabs__class_Oabs(X5,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).
fof(fact_abs__triangle__ineq,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12)),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oabs__class_Oabs(X5,X13),c_Groups_Oabs__class_Oabs(X5,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X14,X11,X12,X13,X54,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X54 != c_Groups_Ozero__class_Ozero(X5)
=> ( ( X13 = X12
& X11 != X14 )
=> c_Groups_Oplus__class_Oplus(X5,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X54),X11)) != c_Groups_Oplus__class_Oplus(X5,X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X54),X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_real__mult__less__iff1,axiom,
! [X27,X24,X56] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X56)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X56))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_nat__power__less__imp__less,axiom,
! [X6,X7,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X7),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X17),X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [X27,X24,X56] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X56)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X56))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [X27,X24,X56] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X56)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X56),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X56),X27))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(fact_mult__le__cancel2,axiom,
! [X19,X21,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X21))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_mult__le__cancel1,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_norm__triangle__ineq2,axiom,
! [X12,X13,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X13),c_RealVector_Onorm__class_Onorm(X5,X12)),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X13,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).
fof(fact_norm__diff__ineq,axiom,
! [X12,X13,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X13),c_RealVector_Onorm__class_Onorm(X5,X12)),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).
fof(fact_norm__triangle__ineq4,axiom,
! [X12,X13,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X13,X12)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X13),c_RealVector_Onorm__class_Onorm(X5,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).
fof(fact_norm__triangle__ineq,axiom,
! [X23,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oplus__class_Oplus(X5,X4,X23)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
fof(fact_natfloor__eq,axiom,
! [X4,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6),X4)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatfloor(X4) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__eq) ).
fof(fact_le__diff__conv2,axiom,
! [X36,X43,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X43)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,X21))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X21),X43) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [X33,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X61,X60)),X33) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X33,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X61,X60)),X33) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_real__add__mult__distrib,axiom,
! [X33,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X61,X60)),X33) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X61),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X60),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_diff__mult__distrib,axiom,
! [X15,X6,X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6)),X15) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X15,X6,X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)),X15) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_norm__power__ineq,axiom,
! [X6,X4,X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
fof(fact_add__less__imp__less__right,axiom,
! [X12,X11,X13,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),c_Groups_Oplus__class_Oplus(X5,X12,X11))
=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__right,axiom,
! [X8,X9,X10,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X10,X9),c_Groups_Oplus__class_Oplus(X5,X8,X9))
<=> c_Orderings_Oord__class_Oless(X5,X10,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [X12,X13,X11,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X11,X13),c_Groups_Oplus__class_Oplus(X5,X11,X12))
=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__cancel__left,axiom,
! [X8,X10,X9,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X9,X10),c_Groups_Oplus__class_Oplus(X5,X9,X8))
<=> c_Orderings_Oord__class_Oless(X5,X10,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__le__imp__le__right,axiom,
! [X12,X11,X13,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),c_Groups_Oplus__class_Oplus(X5,X12,X11))
=> c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__right,axiom,
! [X8,X9,X10,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X10,X9),c_Groups_Oplus__class_Oplus(X5,X8,X9))
<=> c_Orderings_Oord__class_Oless__eq(X5,X10,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [X12,X13,X11,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X11,X13),c_Groups_Oplus__class_Oplus(X5,X11,X12))
=> c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__cancel__left,axiom,
! [X8,X10,X9,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X9,X10),c_Groups_Oplus__class_Oplus(X5,X9,X8))
<=> c_Orderings_Oord__class_Oless__eq(X5,X10,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [X6,X7,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X6)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X15),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X15)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_power__gt1__lemma,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X13)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_zpower__zadd__distrib,axiom,
! [X26,X23,X4] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4),X23)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4),X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_nat__less__real__le,axiom,
! [X18,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X19),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_nat__le__real__less,axiom,
! [X18,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X19),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
fof(fact_self__quotient__aux2,axiom,
! [X81,X54,X13] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
=> ( X13 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X81))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,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,
! [X81,X54,X13] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
=> ( X13 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X81))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X81) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [X12,X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X6)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> X13 = X12 ) ) ) ) ),
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,
! [X7,X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X7),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X13,c_Groups_Oone__class_Oone(X5))),X7) ),
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,
! [X13,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X7)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X13,c_Groups_Oone__class_Oone(X5))),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_mult__right__le__one__le,axiom,
! [X23,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X23)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X23),X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,axiom,
! [X23,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X23)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X4),X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_norm__ratiotest__lemma,axiom,
! [X23,X4,X11,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),c_RealVector_Onorm__class_Onorm(X5,X23)))
=> X4 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
fof(fact_mult__strict__right__mono,axiom,
! [X11,X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X11,X12,X13,X5] :
( class_Rings_Olinordered__comm__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X11,X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_power__mono,axiom,
! [X6,X12,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
fof(fact_mult__right__mono,axiom,
! [X11,X12,X13,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(fact_comm__mult__left__mono,axiom,
! [X11,X12,X13,X5] :
( class_Rings_Oordered__comm__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [X11,X12,X13,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X11,X13,X12,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X13)
=> ( c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X11,X13,X12,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X13)
=> ( c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [X11,X13,X12,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X11,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_mult__left__mono__neg,axiom,
! [X11,X13,X12,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X11,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_le__add__diff,axiom,
! [X7,X6,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X7),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(fact_add__strict__mono,axiom,
! [X14,X11,X12,X13,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless(X5,X11,X14)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),c_Groups_Oplus__class_Oplus(X5,X12,X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X14,X11,X12,X13,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless(X5,X11,X14)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),c_Groups_Oplus__class_Oplus(X5,X12,X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X14,X11,X12,X13,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X11,X14)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),c_Groups_Oplus__class_Oplus(X5,X12,X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__mono,axiom,
! [X14,X11,X12,X13,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X11,X14)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),c_Groups_Oplus__class_Oplus(X5,X12,X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_power__strict__increasing,axiom,
! [X13,X88,X6,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X88)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X13)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X88)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__increasing,axiom,
! [X13,X88,X6,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X88)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),X13)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X88)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(fact_abs__eq__mult,axiom,
! [X12,X13,X5] :
( class_Rings_Oordered__ring__abs(X5)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
| c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Ozero__class_Ozero(X5)) )
& ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
| c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) )
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X13)),c_Groups_Oabs__class_Oabs(X5,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
fof(fact_realpow__num__eq__if,axiom,
! [X7,X6,X5] :
( class_Power_Opower(X5)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X6) = c_Groups_Oone__class_Oone(X5) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(fact_zdiv__mono1,axiom,
! [X12,X73,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,X73)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X73,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
fof(fact_div__le__mono2,axiom,
! [X15,X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X15,X6),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X15,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono2) ).
fof(fact_zdiv__mono1__neg,axiom,
! [X12,X73,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,X73)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,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,X73,X12),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
fof(fact_zadd__zless__mono,axiom,
! [X26,X57,X33,X58] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X58,X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X57,X26)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X58,X57),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X33,X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_diff__less__mono,axiom,
! [X11,X12,X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X13,X11),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(fact_diff__less__mono2,axiom,
! [X20,X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_add__less__mono,axiom,
! [X20,X15,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_add__le__mono,axiom,
! [X20,X15,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X16)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X27,X24,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X27)) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X24 = c_Groups_Ozero__class_Ozero(X5)
& X27 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_rabs__ratiotest__lemma,axiom,
! [X23,X4,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23)))
=> X4 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).
fof(fact_mult_Odiff__right,axiom,
! [X71,X12,X13,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),c_Groups_Ominus__class_Ominus(X5,X12,X71)) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X71)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
fof(fact_mult__right_Odiff,axiom,
! [X23,X4,X72,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X72),c_Groups_Ominus__class_Ominus(X5,X4,X23)) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X72),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X72),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
fof(fact_mult__right_Oadd,axiom,
! [X23,X4,X72,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X72),c_Groups_Oplus__class_Oplus(X5,X4,X23)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X72),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X72),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult_Oadd__right,axiom,
! [X71,X12,X13,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),c_Groups_Oplus__class_Oplus(X5,X12,X71)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X71)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X26,X23,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oplus__class_Oplus(X5,X23,X26)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_mult__less__cancel1,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X19,X21,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X21))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
! [X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X10,X8))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X10)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X13,X12,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X13))
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12))
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_DeMoivre2,axiom,
! [X6,X13,X54] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X54,X13)),X6) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X54),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DeMoivre2) ).
fof(fact_power__commutes,axiom,
! [X6,X13,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X11,X12,X13,X5] :
( class_Groups_Oab__semigroup__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11)) ),
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,
! [X76,X77,X78,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),X77)),X76) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X77),X76)) ),
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,
! [X75,X76,X78,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X76),X75)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),X76)),X75) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_reals__Archimedean6,axiom,
! [X54] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X54)
=> ? [X31] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X54)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X54,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X31)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6) ).
fof(fact_monoseq__def,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Omonoseq(X5,X34)
<=> ( ! [X35,X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X31)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,X35),hAPP(X34,X31)) )
| ! [X35,X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X31)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,X31),hAPP(X34,X35)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monoseq__def) ).
fof(fact_natfloor__div__nat,axiom,
! [X23,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23)
=> c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X23))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X4),X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__div__nat) ).
fof(fact_power__mult,axiom,
! [X6,X7,X13,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X7)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X81,X87,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X87)),X81) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X81)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_zmult__zless__mono2,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X16)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X15)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_real__mult__less__mono2,axiom,
! [X23,X4,X26] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X26)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,X23)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_power__eq__if,axiom,
! [X87,X7] :
( ( X7 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X87),X7) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X7 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X87),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X87),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,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,
! [X21,X43,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,X21))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X21),X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(fact_le__diff__conv,axiom,
! [X36,X21,X43] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,X21),X36)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_mult__le__mono,axiom,
! [X20,X15,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X16)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(fact_add__diff__assoc2,axiom,
! [X17,X16,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X16)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X15),X17) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X17),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc2,axiom,
! [X17,X16,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X16)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X17),X15) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X15),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_diff__add__assoc,axiom,
! [X17,X16,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X16)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X16),X15) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_diff__diff__right,axiom,
! [X17,X16,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X16)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X15)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X15),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(fact_add__diff__assoc,axiom,
! [X17,X16,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X16)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X15)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X16),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [X10,X8] :
( c_Orderings_Oord__class_Oless(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_Divides_Odiv__class_Odiv(tc_Int_Oint,X10,X8))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_neg__imp__zdiv__neg__iff,axiom,
! [X10,X8] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X8,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X10,X8),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
fof(fact_pos__imp__zdiv__neg__iff,axiom,
! [X10,X8] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X10,X8),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
! [X10,X8] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X8,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,X10,X8))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [X36,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X36,X21))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_zdiv__zmult2__eq,axiom,
! [X12,X13,X11] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X11)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
fof(fact_mult__le__0__iff,axiom,
! [X8,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X8),c_Groups_Ozero__class_Ozero(X5))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X10)
& c_Orderings_Oord__class_Oless__eq(X5,X8,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless__eq(X5,X10,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X8) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [X8,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X8))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X10)
& c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X8) )
| ( c_Orderings_Oord__class_Oless__eq(X5,X10,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless__eq(X5,X8,c_Groups_Ozero__class_Ozero(X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [X19,X24] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X24)),X19))
<=> ( X24 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [X60,X61,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X61,X60)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X60)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X60,X61,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X61,X60)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X60)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_diff__mult__distrib2,axiom,
! [X6,X7,X15] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X6,X7,X15] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X7,X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5))),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_nat__mult__div__cancel1,axiom,
! [X6,X7,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X6)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [X27,X24] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X27)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X24 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X27 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(fact_zero__less__power__nat__eq__number__of,axiom,
! [X51,X24] :
( 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),X24),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X51)))
<=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X51) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq__number__of) ).
fof(fact_add__neg__neg,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__nonpos__neg,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__pos__pos,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X13,X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__nonneg__pos,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X13,X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X13,X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X13,X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_natfloor__subtract,axiom,
! [X4,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X13),X4)
=> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X13))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X4),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__subtract) ).
fof(fact_natceiling__subtract,axiom,
! [X4,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X13),X4)
=> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X13))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X4),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__subtract) ).
fof(fact_add__gr__0,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
| 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_add__gr__0) ).
fof(fact_zpower__zpower,axiom,
! [X26,X23,X4] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4),X23)),X26) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23),X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_zmult__assoc,axiom,
! [X59,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X60)),X59) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X60),X59)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_real__mult__assoc,axiom,
! [X59,X60,X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X61),X60)),X59) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X60),X59)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X15,X6,X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6)),X15) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_mult__neg__pos,axiom,
! [X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X13),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_split__mult__neg__le,axiom,
! [X12,X13,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
& c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) )
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12),c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [X12,X13,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [X12,X13,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [X12,X13,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X13),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__pos__pos,axiom,
! [X12,X13,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_less__1__mult,axiom,
! [X6,X7,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X7)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X6)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_split__mult__pos__le,axiom,
! [X12,X13,X5] :
( class_Rings_Oordered__ring(X5)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
& c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12) )
| ( c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) )
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [X12,X13,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_mult__neg__neg,axiom,
! [X12,X13,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [X12,X13,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_add__strict__right__mono,axiom,
! [X11,X12,X13,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),c_Groups_Oplus__class_Oplus(X5,X12,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X11,X12,X13,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X11,X13),c_Groups_Oplus__class_Oplus(X5,X11,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_add__right__mono,axiom,
! [X11,X12,X13,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),c_Groups_Oplus__class_Oplus(X5,X12,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X11,X12,X13,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X11,X13),c_Groups_Oplus__class_Oplus(X5,X11,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
! [X6,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X26),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X26,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
fof(fact_realpow__pos__nth__unique,axiom,
! [X13,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)
=> ? [X3] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3),X6) = X13
& ! [X55] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X55)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X55),X6) = X13 )
=> X55 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth__unique) ).
fof(fact_one__less__power,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X13)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_monoI1,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( ! [X35,X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X31)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,X35),hAPP(X34,X31)) )
=> c_SEQ_Omonoseq(X5,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monoI1) ).
fof(fact_monoI2,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( ! [X35,X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X31)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,X31),hAPP(X34,X35)) )
=> c_SEQ_Omonoseq(X5,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monoI2) ).
fof(fact_incseq__def,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Oincseq(X5,X34)
<=> ! [X35,X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X31)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,X35),hAPP(X34,X31)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incseq__def) ).
fof(fact_decseq__def,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Odecseq(X5,X34)
<=> ! [X35,X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X31)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(X34,X31),hAPP(X34,X35)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decseq__def) ).
fof(fact_pos__add__strict,axiom,
! [X11,X12,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X11)
=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Oplus__class_Oplus(X5,X13,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__strict__increasing2,axiom,
! [X11,X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X11)
=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Oplus__class_Oplus(X5,X13,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X11,X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X11)
=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Oplus__class_Oplus(X5,X13,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__increasing,axiom,
! [X11,X12,X13,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X11)
=> c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Oplus__class_Oplus(X5,X13,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X13,X12,X11,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
=> c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Oplus__class_Oplus(X5,X13,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_of__nat__diff,axiom,
! [X7,X6,X5] :
( class_Rings_Oring__1(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6)) = c_Groups_Ominus__class_Ominus(X5,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__diff) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X16)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X15),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_zadd__left__mono,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X17),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_real__add__left__mono,axiom,
! [X26,X23,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X26,X4),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X26,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_div__le__mono,axiom,
! [X15,X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X15),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X6,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono) ).
fof(fact_diff__le__mono,axiom,
! [X20,X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [X20,X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_add__le__mono1,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_div__add__self1,axiom,
! [X13,X12,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X12 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,c_Groups_Oplus__class_Oplus(X5,X12,X13),X12) = c_Groups_Oplus__class_Oplus(X5,c_Divides_Odiv__class_Odiv(X5,X13,X12),c_Groups_Oone__class_Oone(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self1) ).
fof(fact_div__add__self2,axiom,
! [X13,X12,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X12 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),X12) = c_Groups_Oplus__class_Oplus(X5,c_Divides_Odiv__class_Odiv(X5,X13,X12),c_Groups_Oone__class_Oone(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self2) ).
fof(fact_abs__add__abs,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Oplus__class_Oplus(X5,c_Groups_Oabs__class_Oabs(X5,X13),c_Groups_Oabs__class_Oabs(X5,X12))) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oabs__class_Oabs(X5,X13),c_Groups_Oabs__class_Oabs(X5,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).
fof(fact_div__neg__pos__less0,axiom,
! [X12,X13] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
fof(fact_div__nonneg__neg__le0,axiom,
! [X12,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,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,X13,X12),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,
! [X12,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X23,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> 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,X4,X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X23,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> 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,X4,X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_eq__diff__iff,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X19)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X21) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X21)
<=> X18 = X19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_int__div__less__self,axiom,
! [X15,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X15)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X15),X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).
fof(fact_div__less__dividend,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less__dividend) ).
fof(fact_diff__less,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X10,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X10,X10))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X10) ) ),
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,
! [X10,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X10,X10))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_even__less__0__iff,axiom,
! [X10,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X10,X10),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,X10,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X10,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X10,X10),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,X10,c_Groups_Ozero__class_Ozero(X5)) ) ),
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,
! [X10,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X10,X10),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless__eq(X5,X10,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_rcis__mult,axiom,
! [X12,X97,X13,X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X98,X13)),c_Complex_Orcis(X97,X12)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X98),X97),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rcis__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X11,X12,X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),X11) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),X12) ),
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,
! [X11,X12,X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),X11) = c_Groups_Oplus__class_Oplus(X5,X13,c_Groups_Oplus__class_Oplus(X5,X12,X11)) ),
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,
! [X11,X12,X13,X5] :
( class_Groups_Oab__semigroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),X11) = c_Groups_Oplus__class_Oplus(X5,X13,c_Groups_Oplus__class_Oplus(X5,X12,X11)) ),
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,
! [X14,X11,X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X13,c_Groups_Oplus__class_Oplus(X5,X11,X14)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X11),X14) ),
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,
! [X14,X11,X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X13,c_Groups_Oplus__class_Oplus(X5,X11,X14)) = c_Groups_Oplus__class_Oplus(X5,X11,c_Groups_Oplus__class_Oplus(X5,X13,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_div__mult__mult1__if,axiom,
! [X12,X13,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( ( X11 = c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12)) = c_Groups_Ozero__class_Ozero(X5) )
& ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12)) = c_Divides_Odiv__class_Odiv(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).
fof(fact_div__mult__mult1,axiom,
! [X12,X13,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X12)) = c_Divides_Odiv__class_Odiv(X5,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1) ).
fof(fact_div__mult__mult2,axiom,
! [X12,X13,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X11)) = c_Divides_Odiv__class_Odiv(X5,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult2) ).
fof(fact_less__iff__diff__less__0,axiom,
! [X8,X10,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X10,X8)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ominus__class_Ominus(X5,X10,X8),c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_le__iff__diff__le__0,axiom,
! [X8,X10,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X8)
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,X10,X8),c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_real__mult__order,axiom,
! [X23,X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X23)
=> 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),X4),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [X19,X18] :
( 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),X18),X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
& 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_nat__0__less__mult__iff) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X23,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> 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),X4),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_abs__mult__pos,axiom,
! [X23,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X23)),X4) = c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
fof(fact_le__cube,axiom,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
fof(fact_zdiff__int,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
=> c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__int) ).
fof(fact_real__of__nat__diff,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
=> hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X7),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).
fof(fact_diff__eq__diff__less,axiom,
! [X41,X9,X8,X10,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X10,X8) = c_Groups_Ominus__class_Ominus(X5,X9,X41)
=> ( c_Orderings_Oord__class_Oless(X5,X10,X8)
<=> c_Orderings_Oord__class_Oless(X5,X9,X41) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [X41,X9,X8,X10,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X10,X8) = c_Groups_Ominus__class_Ominus(X5,X9,X41)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X8)
<=> c_Orderings_Oord__class_Oless__eq(X5,X9,X41) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_natfloor__add,axiom,
! [X13,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X13))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X4),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add) ).
fof(fact_natceiling__add,axiom,
! [X13,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X13))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X4),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add) ).
fof(fact_mult__le__mono1,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X75,X76,X78,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X76),X75)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X76),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X78),X75)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_diff__cancel,axiom,
! [X6,X7,X15] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X6)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [X6,X15,X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X15)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__commute,axiom,
! [X15,X16,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X16),X15) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X15),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(fact_diff__diff__left,axiom,
! [X15,X16,X17] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X16),X15) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_zadd__assoc,axiom,
! [X59,X60,X61] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X61,X60),X59) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X61,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X60,X59)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X15,X6,X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6),X15) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [X26,X23,X4] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X26)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X26,X23,X4] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X26)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_zless__add1__eq,axiom,
! [X56,X51] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X56,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,X56)
| X51 = X56 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_add1__zle__eq,axiom,
! [X56,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)),X56)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,X56) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zle__diff1__eq,axiom,
! [X56,X51] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X51,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X56,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,X56) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_zle__add1__eq__le,axiom,
! [X56,X51] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X56,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X51,X56) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
! [X42] :
( ! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
=> hBOOL(hAPP(X42,X3)) )
<=> ! [X3] : hBOOL(hAPP(X42,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).
fof(fact_less__bin__lemma,axiom,
! [X30,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X30)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X21,X30),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,
! [X27,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X27)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X24,X27),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,
! [X18,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_less__add__eq__less,axiom,
! [X6,X7,X20,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X20)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_add__lessD1,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X16),X15)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__leD1,axiom,
! [X6,X15,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X15),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X6,X15,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X15),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_div__mult2__eq,axiom,
! [X11,X12,X13] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X11)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X13,X12),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult2__eq) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X27,X24,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X24)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X27)
=> ( c_Groups_Oplus__class_Oplus(X5,X24,X27) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X24 = c_Groups_Ozero__class_Ozero(X5)
& X27 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_less__nat__number__of,axiom,
! [X67,X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X53),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X67))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X53,X67)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X67) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X53,X67) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__number__of) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X19,X24] :
( 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),X24),X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24)
| X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [X19,X24] :
( 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),X24),X19))
<=> ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_nat__mult__div__cancel__disj,axiom,
! [X6,X7,X15] :
( ( X15 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X6)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X15 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X6)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(fact_of__nat__mult,axiom,
! [X6,X7,X5] :
( class_Rings_Osemiring__1(X5)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X7)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__mult) ).
fof(fact_less__natfloor,axiom,
! [X6,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X4),X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__natfloor) ).
fof(fact_natceiling__le__eq,axiom,
! [X10,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X24),X10)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
fof(fact_le__natfloor__eq,axiom,
! [X10,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_RComplete_Onatfloor(X24))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X10),X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
fof(fact_realpow__pos__nth,axiom,
! [X13,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)
=> ? [X99] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X99)
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X99),X6) = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth) ).
fof(fact_zero__le__power__abs,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oabs__class_Oabs(X5,X13)),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_power__inject__exp,axiom,
! [X19,X18,X10,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X10)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X10),X18) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X10),X19)
<=> X18 = X19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_of__nat__less__iff,axiom,
! [X19,X18,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X18),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).
fof(fact_of__nat__less__imp__less,axiom,
! [X6,X7,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X6))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).
fof(fact_of__nat__le__iff,axiom,
! [X19,X18,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X18),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__le__iff) ).
fof(fact_zero__less__power,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_zero__le__power,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(fact_one__le__power,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),X13)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(fact_natfloor__add__one,axiom,
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
fof(fact_natceiling__add__one,axiom,
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
fof(fact_of__nat__add,axiom,
! [X6,X7,X5] :
( class_Rings_Osemiring__1(X5)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)) = c_Groups_Oplus__class_Oplus(X5,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__add) ).
fof(fact_odd__nonzero,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26),X26) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [X23,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X4,X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_of__nat__aux_Osimps_I1_J,axiom,
! [X36,X37,X5] :
( class_Rings_Osemiring__1(X5)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X37,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36) = X36 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
fof(fact_power_Opower_Opower__0,axiom,
! [X10,X90,X91,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X91,X90),X10),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X91,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
! [X42] :
( ? [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
& hBOOL(hAPP(X42,X3)) )
<=> ? [X3] : hBOOL(hAPP(X42,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).
fof(fact_le__imp__0__less,axiom,
! [X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)
=> 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),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_abs__mult,axiom,
! [X12,X13,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X13)),c_Groups_Oabs__class_Oabs(X5,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).
fof(fact_real__natfloor__add__one__gt,axiom,
! [X4] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X4)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
! [X23,X4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
fof(fact_zmult__int,axiom,
! [X6,X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__int) ).
fof(fact_int__mult,axiom,
! [X6,X7] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__mult) ).
fof(fact_real__of__nat__mult,axiom,
! [X6,X7] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X7)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
fof(fact_norm__minus__commute,axiom,
! [X12,X13,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X13,X12)) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X12,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(fact_abs__minus__commute,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X13,X12)) = c_Groups_Oabs__class_Oabs(X5,c_Groups_Ominus__class_Ominus(X5,X12,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).
fof(fact_norm__mult,axiom,
! [X23,X4,X5] :
( class_RealVector_Oreal__normed__div__algebra(X5)
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)),c_RealVector_Onorm__class_Onorm(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).
fof(fact_zless__imp__add1__zle,axiom,
! [X26,X33] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X33,X26)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X33,c_Groups_Oone__class_Oone(tc_Int_Oint)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_of__nat__power,axiom,
! [X6,X7,X5] :
( class_Rings_Osemiring__1(X5)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X7)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__power) ).
fof(fact_le__add__diff__inverse2,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),X6) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_diff__diff__cancel,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X6)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X17)) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_le__add__diff__inverse,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_arith__simps_I32_J,axiom,
! [X33,X49,X5] :
( class_Int_Onumber__ring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X5,X49)),c_Int_Onumber__class_Onumber__of(X5,X33)) = c_Int_Onumber__class_Onumber__of(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
fof(fact_number__of__mult,axiom,
! [X33,X49,X5] :
( class_Int_Onumber__ring(X5)
=> c_Int_Onumber__class_Onumber__of(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X5,X49)),c_Int_Onumber__class_Onumber__of(X5,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__mult) ).
fof(fact_le__funD,axiom,
! [X24,X1,X2,X5,X25] :
( class_Orderings_Oord(X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X25),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X25,hAPP(X2,X24),hAPP(X1,X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X24,X1,X2,X5,X25] :
( class_Orderings_Oord(X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X25),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X25,hAPP(X2,X24),hAPP(X1,X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_less__imp__diff__less,axiom,
! [X6,X15,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X15)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X6),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_trans__less__add1,axiom,
! [X7,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X26,X23,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X23)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add2,axiom,
! [X7,X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X23,X26,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X26)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X26,X23,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add1,axiom,
! [X7,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X23,X26,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X26)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_trans__le__add2,axiom,
! [X7,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_zless__int,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__int) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J,axiom,
! [X27,X24] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
fof(fact_real__of__nat__less__iff,axiom,
! [X18,X19] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X19),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
fof(fact_zle__int,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__int) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J,axiom,
! [X27,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).
fof(fact_real__of__nat__le__iff,axiom,
! [X18,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X19),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
! [X23,X4] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).
fof(fact_zadd__int,axiom,
! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
! [X23,X4] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
fof(fact_zdiv__int,axiom,
! [X12,X13] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X13,X12)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__int) ).
fof(fact_real__of__nat__add,axiom,
! [X6,X7] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X7),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
fof(fact_zero__le__zpower__abs,axiom,
! [X6,X4] : 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4)),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X19,X18,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X19)
<=> X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_less__number__of,axiom,
! [X27,X24,X5] :
( ( class_Int_Onumber__ring(X5)
& class_Rings_Olinordered__idom(X5) )
=> ( c_Orderings_Oord__class_Oless(X5,c_Int_Onumber__class_Onumber__of(X5,X24),c_Int_Onumber__class_Onumber__of(X5,X27))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of) ).
fof(fact_le__number__of,axiom,
! [X27,X24,X5] :
( ( class_Int_Onumber__ring(X5)
& class_Rings_Olinordered__idom(X5) )
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Int_Onumber__class_Onumber__of(X5,X24),c_Int_Onumber__class_Onumber__of(X5,X27))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [X6,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> 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),X4),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_order__less__trans,axiom,
! [X26,X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> ( c_Orderings_Oord__class_Oless(X5,X23,X26)
=> c_Orderings_Oord__class_Oless(X5,X4,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X26,X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X23)
=> ( c_Orderings_Oord__class_Oless(X5,X23,X26)
=> c_Orderings_Oord__class_Oless(X5,X4,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X26,X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,X26)
=> c_Orderings_Oord__class_Oless(X5,X4,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X26,X4,X23,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X23,X4)
=> ( c_Orderings_Oord__class_Oless(X5,X26,X23)
=> c_Orderings_Oord__class_Oless(X5,X26,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_xt1_I8_J,axiom,
! [X26,X4,X23,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,X4)
=> ( c_Orderings_Oord__class_Oless(X5,X26,X23)
=> c_Orderings_Oord__class_Oless(X5,X26,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X26,X4,X23,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X23,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X26,X23)
=> c_Orderings_Oord__class_Oless(X5,X26,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__trans,axiom,
! [X26,X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,X26)
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X26,X4,X23,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X26,X23)
=> c_Orderings_Oord__class_Oless__eq(X5,X26,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_div__mult__self1__is__m,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X7),X6) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).
fof(fact_div__mult__self__is__m,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6),X6) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).
fof(fact_add__number__of__eq,axiom,
! [X33,X49,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Int_Onumber__class_Onumber__of(X5,X49),c_Int_Onumber__class_Onumber__of(X5,X33)) = c_Int_Onumber__class_Onumber__of(X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__eq) ).
fof(fact_number__of__diff,axiom,
! [X33,X49,X5] :
( class_Int_Onumber__ring(X5)
=> c_Int_Onumber__class_Onumber__of(X5,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X49,X33)) = c_Groups_Ominus__class_Ominus(X5,c_Int_Onumber__class_Onumber__of(X5,X49),c_Int_Onumber__class_Onumber__of(X5,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__diff) ).
fof(fact_number__of__add,axiom,
! [X33,X49,X5] :
( class_Int_Onumber__ring(X5)
=> c_Int_Onumber__class_Onumber__of(X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X33)) = c_Groups_Oplus__class_Oplus(X5,c_Int_Onumber__class_Onumber__of(X5,X49),c_Int_Onumber__class_Onumber__of(X5,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).
fof(fact_zdiv__eq__0__iff,axiom,
! [X21,X36] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X36,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( X21 = 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),X36)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X36,X21) )
| ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X36,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_div__pos__pos__trivial,axiom,
! [X12,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X13)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,X12)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
fof(fact_div__neg__neg__trivial,axiom,
! [X12,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X13)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X12) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
fof(fact_power__abs,axiom,
! [X6,X13,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oabs__class_Oabs(X5,X13)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).
fof(fact_le__imp__diff__is__add,axiom,
! [X21,X43,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X43)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,X36) = X21
<=> X43 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_less__imp__of__nat__less,axiom,
! [X6,X7,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless(X5,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).
fof(fact_zle__iff__zadd,axiom,
! [X56,X51] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X51,X56)
<=> ? [X31] : X56 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).
fof(fact_norm__power,axiom,
! [X6,X4,X5] :
( class_RealVector_Oreal__normed__div__algebra(X5)
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power) ).
fof(fact_zle__trans,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,X16)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X15)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(fact_real__le__trans,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X16)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X15)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_le__trans,axiom,
! [X15,X16,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X16)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X15)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_of__nat__0__less__iff,axiom,
! [X19,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X19))
<=> 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_of__nat__0__less__iff) ).
fof(fact_times__numeral__code_I5_J,axiom,
! [X33,X49] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X33)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
! [X6,X4] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4)),X6) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
fof(fact_zpower__int,axiom,
! [X6,X7] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7)),X6) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__int) ).
fof(fact_power__real__of__nat,axiom,
! [X6,X7] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X7)),X6) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
fof(fact_int__power,axiom,
! [X6,X7] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7)),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power) ).
fof(fact_real__of__nat__power,axiom,
! [X6,X7] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X7)),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
fof(fact_plus__numeral__code_I9_J,axiom,
! [X33,X49] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X33)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [X4] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_less__number__of__int__code,axiom,
! [X30,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X21),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X30))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).
fof(fact_less__eq__number__of__int__code,axiom,
! [X30,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X21),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X30))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).
fof(fact_subseq__def,axiom,
! [X2] :
( c_SEQ_Osubseq(X2)
<=> ! [X35,X31] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X31)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X35),hAPP(X2,X31)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__def) ).
fof(fact_real__natfloor__gt__diff__one,axiom,
! [X4] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).
fof(fact_less__special_I1_J,axiom,
! [X27,X5] :
( ( class_Int_Onumber__ring(X5)
& class_Rings_Olinordered__idom(X5) )
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Int_Onumber__class_Onumber__of(X5,X27))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I1_J) ).
fof(fact_le__special_I1_J,axiom,
! [X27,X5] :
( ( class_Int_Onumber__ring(X5)
& class_Rings_Olinordered__idom(X5) )
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Int_Onumber__class_Onumber__of(X5,X27))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I1_J) ).
fof(fact_less__special_I3_J,axiom,
! [X24,X5] :
( ( class_Int_Onumber__ring(X5)
& class_Rings_Olinordered__idom(X5) )
=> ( c_Orderings_Oord__class_Oless(X5,c_Int_Onumber__class_Onumber__of(X5,X24),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,c_Int_OPls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I3_J) ).
fof(fact_le__special_I3_J,axiom,
! [X24,X5] :
( ( class_Int_Onumber__ring(X5)
& class_Rings_Olinordered__idom(X5) )
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Int_Onumber__class_Onumber__of(X5,X24),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,c_Int_OPls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I3_J) ).
fof(fact_zero__less__two,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
! [X23,X4] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).
fof(fact_zero__less__int__conv,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19))
<=> 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__int__conv) ).
fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X19))
<=> 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_real__of__nat__gt__zero__cancel__iff) ).
fof(fact_natceiling__le,axiom,
! [X13,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X13))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le) ).
fof(fact_le__natfloor,axiom,
! [X13,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X4),X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_RComplete_Onatfloor(X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor) ).
fof(fact_nat__less__cases,axiom,
! [X42,X19,X18] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19)
=> hBOOL(hAPP(hAPP(X42,X19),X18)) )
=> ( ( X18 = X19
=> hBOOL(hAPP(hAPP(X42,X19),X18)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
=> hBOOL(hAPP(hAPP(X42,X19),X18)) )
=> hBOOL(hAPP(hAPP(X42,X19),X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_natfloor__power,axiom,
! [X6,X4] :
( X4 = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X4))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X4),X6)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X4)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__power) ).
fof(fact_abs__mult__self,axiom,
! [X13,X5] :
( class_Rings_Olinordered__idom(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oabs__class_Oabs(X5,X13)),c_Groups_Oabs__class_Oabs(X5,X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).
fof(fact_abs__le__D1,axiom,
! [X12,X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X13),X12)
=> c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).
fof(fact_BseqD,axiom,
! [X34,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_SEQ_OBseq(X5,X34)
=> ? [X62] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X62)
& ! [X31] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(X34,X31)),X62) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_BseqD) ).
fof(fact_real__natfloor__le,axiom,
! [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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X4)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
fof(fact_diff__eq__diff__eq,axiom,
! [X41,X9,X8,X10,X5] :
( class_Groups_Oab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X10,X8) = c_Groups_Ominus__class_Ominus(X5,X9,X41)
=> ( X10 = X8
<=> X9 = X41 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_order__eq__iff,axiom,
! [X27,X24,X5] :
( class_Orderings_Oorder(X5)
=> ( X24 = X27
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
& c_Orderings_Oord__class_Oless__eq(X5,X27,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__antisym__conv,axiom,
! [X24,X27,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
<=> X24 = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X23,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,X4)
=> X4 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X4,X23,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X23)
=> X4 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_less__add__one,axiom,
! [X13,X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,X13,c_Groups_Oplus__class_Oplus(X5,X13,c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_add__right__cancel,axiom,
! [X9,X10,X8,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X8,X10) = c_Groups_Oplus__class_Oplus(X5,X9,X10)
<=> X8 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__right__imp__eq,axiom,
! [X11,X13,X12,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X12,X13) = c_Groups_Oplus__class_Oplus(X5,X11,X13)
=> X12 = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [X11,X12,X13,X5] :
( class_Groups_Ocancel__ab__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X13,X12) = c_Groups_Oplus__class_Oplus(X5,X13,X11)
=> X12 = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X9,X8,X10,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X10,X8) = c_Groups_Oplus__class_Oplus(X5,X10,X9)
<=> X8 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [X11,X12,X13,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X13,X12) = c_Groups_Oplus__class_Oplus(X5,X13,X11)
=> X12 = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_abs__zmult__eq__1,axiom,
! [X6,X7] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7),X6)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X7) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
fof(fact_power__eq__0__iff__number__of,axiom,
! [X51,X10,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Omult__zero(X5)
& class_Rings_Ono__zero__divisors(X5)
& class_Rings_Ozero__neq__one(X5) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X51)) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
& c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X51) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff__number__of) ).
fof(fact_diffs0__imp__equal,axiom,
! [X6,X7] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_less__0__number__of,axiom,
! [X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X53))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__0__number__of) ).
fof(fact_expi__add,axiom,
! [X12,X13] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X13,X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X13)),c_Complex_Oexpi(X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expi__add) ).
fof(fact_div__mult__self1__is__id,axiom,
! [X13,X12,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X12 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X13),X12) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).
fof(fact_div__mult__self2__is__id,axiom,
! [X13,X12,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X12 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12),X12) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).
fof(fact_zero__le__square,axiom,
! [X13,X5] :
( class_Rings_Olinordered__ring(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(fact_zle__antisym,axiom,
! [X33,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X26)
=> X26 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(fact_real__le__antisym,axiom,
! [X33,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X33,X26)
=> X26 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_le__antisym,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
=> X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_add__diff__cancel,axiom,
! [X12,X13,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,c_Groups_Oplus__class_Oplus(X5,X13,X12),X12) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X12,X13,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ominus__class_Ominus(X5,X13,X12),X12) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18),X19) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X18 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X19 = 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,
! [X19,X21,X18] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X21)
<=> X18 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X19,X18,X21] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X19)
<=> X18 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_le__Suc__ex__iff,axiom,
! [X30,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X30)
<=> ? [X31] : X30 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_le__iff__add,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19)
<=> ? [X22] : X19 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_diff__add__0,axiom,
! [X7,X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X7)) = 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,
! [X7,X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X7),X6) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6),X6) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_div__le__dividend,axiom,
! [X6,X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).
fof(fact_diff__le__self,axiom,
! [X6,X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(fact_le__add1,axiom,
! [X7,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X7,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_le__natfloor__eq__one,axiom,
! [X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X24))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_natceiling__le__eq__one,axiom,
! [X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X24),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
fof(fact_zero__less__abs__iff,axiom,
! [X10,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oabs__class_Oabs(X5,X10))
<=> X10 != c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
fof(fact_zero__less__imp__eq__int,axiom,
! [X15] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X15)
=> ? [X31] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31)
& X15 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).
fof(fact_real__mult__right__cancel,axiom,
! [X8,X10,X9] :
( X9 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X8),X9)
<=> X10 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_mult__cancel2,axiom,
! [X19,X21,X18] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X21)
<=> ( X18 = X19
| X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(fact_real__mult__left__cancel,axiom,
! [X8,X10,X9] :
( X9 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X8)
<=> X10 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [X19,X18,X21] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X19)
<=> ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_mult__cancel1,axiom,
! [X19,X18,X21] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X19)
<=> ( X18 = X19
| X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_tsub__eq,axiom,
! [X4,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X4)
=> c_Nat__Transfer_Otsub(X4,X23) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__eq) ).
fof(fact_xt1_I11_J,axiom,
! [X13,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
=> ( X13 != X12
=> c_Orderings_Oord__class_Oless(X5,X12,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X12,X13,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( X13 != X12
=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X23,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X23)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
| X4 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X12,X13,X5] :
( class_Orderings_Oorder(X5)
=> ( X13 != X12
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__less,axiom,
! [X27,X24,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
<=> ( c_Orderings_Oord__class_Oless(X5,X24,X27)
| X24 = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__le,axiom,
! [X27,X24,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
& X24 != X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_xt1_I12_J,axiom,
! [X12,X13,X5] :
( class_Orderings_Oorder(X5)
=> ( X13 != X12
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
=> c_Orderings_Oord__class_Oless(X5,X12,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_natfloor__mono,axiom,
! [X23,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X4),c_RComplete_Onatfloor(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).
fof(fact_natceiling__mono,axiom,
! [X23,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4),c_RComplete_Onatceiling(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__mono) ).
fof(fact_abs__le__zero__iff,axiom,
! [X10,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X10),c_Groups_Ozero__class_Ozero(X5))
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_order__less__imp__le,axiom,
! [X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X56)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X56) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zero__less__norm__iff,axiom,
! [X24,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X24))
<=> X24 != c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_le__square,axiom,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
fof(fact_int__le__0__conv,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__le__0__conv) ).
fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X19 = 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_norm__le__zero__iff,axiom,
! [X24,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X24),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X24 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
fof(fact_diff__is__0__eq,axiom,
! [X19,X18] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_zless__le,axiom,
! [X51,X56] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X56,X51)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X56,X51)
& X56 != X51 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_less__eq__real__def,axiom,
! [X27,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X27)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24,X27)
| X24 = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_real__less__def,axiom,
! [X27,X24] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24,X27)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X27)
& X24 != X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(fact_nat__less__le,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19)
& X18 != X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X19,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19)
| X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_le__neq__implies__less,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> ( X7 != X6
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_div__less,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).
fof(fact_diff__is__0__eq_H,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_less__imp__le__nat,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X6,X7] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
| X7 = X6 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X23,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_int__Suc0__eq__1,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).
fof(fact_real__of__nat__one,axiom,
hAPP(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_power__0__left__number__of,axiom,
! [X33,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Osemiring__0(X5) )
=> ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X33) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X33)) = c_Groups_Oone__class_Oone(X5) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X33) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X33)) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left__number__of) ).
fof(fact_zabs__less__one__iff,axiom,
! [X56] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X56),c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> X56 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__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_power__eq__0__iff,axiom,
! [X19,X10,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Omult__zero(X5)
& class_Rings_Ono__zero__divisors(X5)
& class_Rings_Ozero__neq__one(X5) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X10),X19) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
& X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_linorder__neq__iff,axiom,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( X24 != X27
<=> ( c_Orderings_Oord__class_Oless(X5,X24,X27)
| c_Orderings_Oord__class_Oless(X5,X27,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
| X4 = X23
| c_Orderings_Oord__class_Oless(X5,X23,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_abs__of__pos,axiom,
! [X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> c_Groups_Oabs__class_Oabs(X5,X13) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).
fof(fact_abs__of__nonneg,axiom,
! [X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X13)
=> c_Groups_Oabs__class_Oabs(X5,X13) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_linorder__le__less__linear,axiom,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X23)
| c_Orderings_Oord__class_Oless(X5,X23,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_linorder__linear,axiom,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X23)
| c_Orderings_Oord__class_Oless__eq(X5,X23,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X11,X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X13,X11) = c_Groups_Oplus__class_Oplus(X5,X11,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X12,X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_zless__linear,axiom,
! [X23,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X23)
| X4 = X23
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X19,X18] :
( X18 != X19
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_zle__linear,axiom,
! [X33,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X33)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(fact_real__le__linear,axiom,
! [X33,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X33)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X33,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_nat__le__linear,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_divisors__zero,axiom,
! [X12,X13,X5] :
( class_Rings_Ono__zero__divisors(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12) = c_Groups_Ozero__class_Ozero(X5)
=> ( X13 = c_Groups_Ozero__class_Ozero(X5)
| X12 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_no__zero__divisors,axiom,
! [X12,X13,X5] :
( class_Rings_Ono__zero__divisors(X5)
=> ( X13 != c_Groups_Ozero__class_Ozero(X5)
=> ( X12 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X12) != c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_mult__eq__0__iff,axiom,
! [X8,X10,X5] :
( class_Rings_Oring__no__zero__divisors(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X8) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
| X8 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_zero__le__imp__of__nat,axiom,
! [X7,X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).
fof(fact_of__nat__0__le__iff,axiom,
! [X6,X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).
fof(fact_zadd__commute,axiom,
! [X33,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X33) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X33,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_double__eq__0__iff,axiom,
! [X10,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X10,X10) = c_Groups_Ozero__class_Ozero(X5)
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X10,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X10,X10)
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [X8,X10,X5] :
( class_Groups_Oab__group__add(X5)
=> ( X10 = X8
<=> c_Groups_Ominus__class_Ominus(X5,X10,X8) = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [X8,X10,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X10,X8) = c_Groups_Ozero__class_Ozero(X5)
<=> X10 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_field__power__not__zero,axiom,
! [X6,X13,X5] :
( class_Rings_Oring__1__no__zero__divisors(X5)
=> ( X13 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),X6) != c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_add__0__iff,axiom,
! [X10,X8,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X8 = c_Groups_Oplus__class_Oplus(X5,X8,X10)
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_real__natceiling__ge,axiom,
! [X4] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X23,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> X23 != X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X23,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> X4 != X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X23,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> X4 != X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_eq__number__of__0,axiom,
! [X53] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X53) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,c_Int_OPls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__0) ).
fof(fact_eq__0__number__of,axiom,
! [X53] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X53)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,c_Int_OPls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__0__number__of) ).
fof(fact_natfloor__neg,axiom,
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatfloor(X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__neg) ).
fof(fact_natceiling__neg,axiom,
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatceiling(X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__neg) ).
fof(fact_neq0__conv,axiom,
! [X19] :
( X19 != 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_neq0__conv) ).
fof(fact_abs__ge__zero,axiom,
! [X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oabs__class_Oabs(X5,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_neg__def,axiom,
! [X66] :
( c_Nat__Numeral_Oneg(X66)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X66,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__def) ).
fof(fact_le__0__eq,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_zmult__commute,axiom,
! [X33,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_real__mult__commute,axiom,
! [X33,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X33),X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X6,X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_add__is__0,axiom,
! [X19,X18] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_gr__implies__not0,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_norm__number__of,axiom,
! [X33,X5] :
( ( class_Int_Onumber__ring(X5)
& class_RealVector_Oreal__normed__algebra__1(X5) )
=> c_RealVector_Onorm__class_Onorm(X5,c_Int_Onumber__class_Onumber__of(X5,X33)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__number__of) ).
fof(fact_norm__ge__zero,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(fact_power__0__left,axiom,
! [X6,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Osemiring__0(X5) )
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),X6) = c_Groups_Oone__class_Oone(X5) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),X6) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(fact_add__eq__self__zero,axiom,
! [X6,X7] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6) = X7
=> X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_zero__zle__int,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__zle__int) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
! [X26] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(fact_abs__ge__self,axiom,
! [X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,X13,c_Groups_Oabs__class_Oabs(X5,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).
fof(fact_less__not__refl3,axiom,
! [X39,X40] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X39)
=> X40 != X39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X7)
=> X7 != X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_g_I1_J,axiom,
! [X31] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(X31)),v_r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_g_I1_J) ).
fof(fact_seq__suble,axiom,
! [X19,X2] :
( c_SEQ_Osubseq(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,hAPP(X2,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_seq__suble) ).
fof(fact_bin__less__0__simps_I1_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
fof(fact_add__numeral__0,axiom,
! [X13,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Int_Onumber__class_Onumber__of(X5,c_Int_OPls),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).
fof(fact_add__numeral__0__right,axiom,
! [X13,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oplus__class_Oplus(X5,X13,c_Int_Onumber__class_Onumber__of(X5,c_Int_OPls)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).
fof(fact_mult__is__0,axiom,
! [X19,X18] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19 = 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,
! [X6,X7] :
( X7 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X6)
=> ( X6 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X7 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [X19,X18] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X19) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X19 = 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,
! [X19,X18] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X19)
<=> ( X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X19 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_abs__of__nat,axiom,
! [X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X6)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nat) ).
fof(fact_rel__simps_I2_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).
fof(fact_power__power__power,axiom,
! [X5] :
( class_Power_Opower(X5)
=> c_Power_Opower__class_Opower(X5) = c_Power_Opower_Opower(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Otimes__class_Otimes(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(fact_norm__of__nat,axiom,
! [X6,X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X6)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__of__nat) ).
fof(fact_power__one,axiom,
! [X6,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oone__class_Oone(X5)),X6) = c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_mult__zero__left,axiom,
! [X13,X5] :
( class_Rings_Omult__zero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X13) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_mult_Ozero__left,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X12) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_mult__left_Ozero,axiom,
! [X23,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X23) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X13) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_zero__less__one,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_zero__le__one,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_of__nat__eq__iff,axiom,
! [X19,X18,X5] :
( class_Nat_Osemiring__char__0(X5)
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X18) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X19)
<=> X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).
fof(fact_mult__1,axiom,
! [X13,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [X13,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_div__0,axiom,
! [X13,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Odiv(X5,c_Groups_Ozero__class_Ozero(X5),X13) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).
fof(fact_div__by__0,axiom,
! [X13,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Odiv(X5,X13,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).
fof(fact_div__self,axiom,
! [X13,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X13 != c_Groups_Ozero__class_Ozero(X5)
=> c_Divides_Odiv__class_Odiv(X5,X13,X13) = c_Groups_Oone__class_Oone(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__self) ).
fof(fact_mult__zero__right,axiom,
! [X13,X5] :
( class_Rings_Omult__zero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_mult_Ozero__right,axiom,
! [X13,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_mult__right_Ozero,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_add__0,axiom,
! [X13,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [X13,X5] :
( class_Groups_Omonoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_div__by__1,axiom,
! [X13,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Odiv(X5,X13,c_Groups_Oone__class_Oone(X5)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).
fof(fact_diff__0__right,axiom,
! [X13,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X13,c_Groups_Ozero__class_Ozero(X5)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X13,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X13,c_Groups_Ozero__class_Ozero(X5)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [X13,X5] :
( class_Groups_Omonoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X13,c_Groups_Ozero__class_Ozero(X5)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X13,c_Groups_Ozero__class_Ozero(X5)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_power__0,axiom,
! [X13,X5] :
( class_Power_Opower(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X13,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),c_Groups_Oone__class_Oone(X5)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [X13,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),c_Groups_Oone__class_Oone(X5)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),c_Groups_Oone__class_Oone(X5)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_diff__self,axiom,
! [X13,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X13,X13) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_order__eq__refl,axiom,
! [X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( X4 = X23
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_power__one__right,axiom,
! [X13,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_zero__le__natfloor,axiom,
! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
fof(fact_zero__le__natceiling,axiom,
! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
fof(fact_order__refl,axiom,
! [X4,X5] :
( class_Orderings_Opreorder(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_abs__int__eq,axiom,
! [X7] : c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__int__eq) ).
fof(fact_abs__real__of__nat__cancel,axiom,
! [X4] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X4)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
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_abs__idempotent,axiom,
! [X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Oabs__class_Oabs(X5,X13)) = c_Groups_Oabs__class_Oabs(X5,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).
fof(fact_eq__number__of,axiom,
! [X27,X24,X5] :
( ( class_Int_Onumber__ring(X5)
& class_Int_Oring__char__0(X5) )
=> ( c_Int_Onumber__class_Onumber__of(X5,X24) = c_Int_Onumber__class_Onumber__of(X5,X27)
<=> X24 = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of) ).
fof(fact_gr0I,axiom,
! [X6] :
( X6 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_abs__norm__cancel,axiom,
! [X13,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X13)) = c_RealVector_Onorm__class_Onorm(X5,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_zdiv__self,axiom,
! [X13] :
( X13 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X13,X13) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).
fof(fact_zdiv__zero,axiom,
! [X12] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).
fof(fact_diff__0__eq__0,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_neg__imp__number__of__eq__0,axiom,
! [X49] :
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__number__of__eq__0) ).
fof(fact_zadd__0,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_zadd__0__right,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_eq__imp__le,axiom,
! [X6,X7] :
( X7 = X6
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J,axiom,
! [X27,X24] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27)
<=> X24 = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
fof(fact_int__int__eq,axiom,
! [X19,X18] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19)
<=> X18 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__int__eq) ).
fof(fact_real__of__nat__inject,axiom,
! [X18,X19] :
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X19) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18)
<=> X19 = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
fof(fact_diff__self__eq__0,axiom,
! [X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X7) = 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,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
fof(fact_zmult__1,axiom,
! [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_real__mult__1,axiom,
! [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X26) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_nat__mult__1,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_zle__refl,axiom,
! [X33] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(fact_real__le__refl,axiom,
! [X33] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X33,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(fact_le__refl,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_add__Pls,axiom,
! [X15] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X15) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(fact_diff__bin__simps_I1_J,axiom,
! [X15] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X15,c_Int_OPls) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).
fof(fact_add__Pls__right,axiom,
! [X15] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,c_Int_OPls) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_mult__0__right,axiom,
! [X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),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_complex__mod__rcis,axiom,
! [X13,X54] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X54,X13)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X54),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__rcis) ).
fof(fact_zmult__1__right,axiom,
! [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_psize__eq__0__iff,axiom,
! [X50,X5] :
( class_Groups_Ozero(X5)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X5,X50) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X50 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_incseq__imp__monoseq,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Oincseq(X5,X34)
=> c_SEQ_Omonoseq(X5,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incseq__imp__monoseq) ).
fof(fact_decseq__imp__monoseq,axiom,
! [X34,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SEQ_Odecseq(X5,X34)
=> c_SEQ_Omonoseq(X5,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decseq__imp__monoseq) ).
fof(fact_mult__Pls,axiom,
! [X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X33) = c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls) ).
fof(fact_abs__eq__0,axiom,
! [X10,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Groups_Oabs__class_Oabs(X5,X10) = c_Groups_Ozero__class_Ozero(X5)
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).
fof(fact_natfloor__number__of__eq,axiom,
! [X6] : c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X6)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__number__of__eq) ).
fof(fact_natceiling__number__of__eq,axiom,
! [X6] : c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X6)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__number__of__eq) ).
fof(fact_norm__eq__zero,axiom,
! [X24,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_RealVector_Onorm__class_Onorm(X5,X24) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X24 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
fof(fact_not__neg__number__of__Pls,axiom,
~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__number__of__Pls) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X101,X100] :
( class_Orderings_Oorder(X100)
=> class_Orderings_Oorder(tc_fun(X101,X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X101,X100] :
( class_Orderings_Oord(X100)
=> class_Orderings_Oord(tc_fun(X101,X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X101,X100] :
( class_Orderings_Opreorder(X100)
=> class_Orderings_Opreorder(tc_fun(X101,X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(fact_natfloor__real__of__nat,axiom,
! [X6] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
fof(fact_natceiling__real__of__nat,axiom,
! [X6] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6)) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
fof(fact_int__eq__0__conv,axiom,
! [X19] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
fof(fact_real__of__nat__zero__iff,axiom,
! [X19] :
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X19) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
fof(fact_of__nat__0,axiom,
! [X5] :
( class_Rings_Osemiring__1(X5)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0) ).
fof(fact_of__nat__1,axiom,
! [X5] :
( class_Rings_Osemiring__1(X5)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__1) ).
fof(fact_abs__zero,axiom,
! [X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).
fof(fact_abs__one,axiom,
! [X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).
fof(fact_norm__zero,axiom,
! [X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(fact_norm__one,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).
fof(fact_real__norm__def,axiom,
! [X54] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X54) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X54),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_number__of__Pls,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Int_Onumber__class_Onumber__of(X5,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Pls) ).
fof(fact_semiring__norm_I112_J,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Int_Onumber__class_Onumber__of(X5,c_Int_OPls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(fact_cis__zero,axiom,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cis__zero) ).
fof(fact_zero__neq__one,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Ozero__class_Ozero(X5) != c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Oone__class_Oone(X5) != c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(fact_complex__i__not__number__of,axiom,
! [X33] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__number__of) ).
fof(fact_rcis__zero__mod,axiom,
! [X13] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rcis__zero__mod) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [X100] :
( class_Rings_Ocomm__ring(X100)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__0(X100)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [X100] :
( class_Groups_Ocancel__comm__monoid__add(X100)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [X100] :
( class_Rings_Oidom(X100)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
! [X100] :
( class_Fields_Ofield(X100)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
! [X100] :
( class_Rings_Oidom(X100)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X100)) ),
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,
! [X100] :
( class_Rings_Ocomm__ring__1(X100)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__0(X100)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__1(X100)
=> class_Power_Opower(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
! [X100] :
( class_Rings_Ocomm__ring__1(X100)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [X100] :
( class_Rings_Ocomm__ring(X100)
=> class_Rings_Oring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__1(X100)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__1(X100)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Nat_Osemiring__char__0,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Nat_Osemiring__char__0) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__0(X100)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__0(X100)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__0(X100)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
! [X100] :
( class_Rings_Oidom(X100)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
! [X100] :
( class_Rings_Oidom(X100)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__0(X100)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Int_Onumber__ring,axiom,
! [X100] :
( class_Rings_Ocomm__ring__1(X100)
=> class_Int_Onumber__ring(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(arity_Polynomial__Opoly__Int_Onumber,axiom,
! [X100] :
( class_Rings_Ocomm__ring__1(X100)
=> class_Int_Onumber(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__1(X100)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [X100] :
( class_Rings_Oidom(X100)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [X100] :
( class_Groups_Ocomm__monoid__add(X100)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [X100] :
( class_Groups_Ocomm__monoid__add(X100)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [X100] :
( class_Groups_Oab__group__add(X100)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [X100] :
( class_Groups_Oab__group__add(X100)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [X100] :
( class_Groups_Ozero(X100)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__1,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__1(X100)
=> class_Rings_Osemiring__1(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__1) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__1(X100)
=> class_Groups_Oone(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [X100] :
( class_Rings_Ocomm__semiring__1(X100)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
! [X100] :
( class_Groups_Ocomm__monoid__add(X100)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
! [X100] :
( class_Groups_Ocancel__comm__monoid__add(X100)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
! [X100] :
( class_Groups_Ocancel__comm__monoid__add(X100)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X100)) ),
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,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [X100] :
( class_Rings_Olinordered__idom(X100)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(fact_number__of__is__id,axiom,
! [X15] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(fact_not__neg__0,axiom,
~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__0) ).
fof(fact_not__neg__1,axiom,
~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__1) ).
fof(fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) ).
fof(fact_number__of2,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of2) ).
fof(fact_wr,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wr) ).
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_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_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_d_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d_I1_J) ).
fof(fact_rp,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp) ).
fof(fact_rel__simps_I19_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).
fof(fact_int__0,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0) ).
fof(fact_int__1,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__1) ).
fof(fact_real__of__nat__zero,axiom,
hAPP(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_real__of__nat__1,axiom,
hAPP(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_transfer__int__nat__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
fof(fact_transfer__int__nat__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
fof(fact_nat__number__of__Pls,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).
fof(fact_zero__is__num__zero,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).
fof(fact_semiring__norm_I113_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).
fof(fact_expi__zero,axiom,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expi__zero) ).
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_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_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_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_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_real__of__nat__def,axiom,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__def) ).
fof(fact_real__eq__of__nat,axiom,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__eq__of__nat) ).
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(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(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__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__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_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_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_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_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__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_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_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_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__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__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
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_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_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_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_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_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_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__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_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_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_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__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__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_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_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__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_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
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_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_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_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_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,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(arity_RealDef__Oreal__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Nat_Osemiring__char__0) ).
fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
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__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_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_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_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_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_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_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_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_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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(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_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
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__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_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(arity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(arity_Complex__Ocomplex__Int_Onumber,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).
fof(arity_Int__Oint__Int_Onumber,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(arity_RealDef__Oreal__Int_Onumber,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
fof(arity_Nat__Onat__Int_Onumber,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
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_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_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_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_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_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_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_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__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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__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_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_Complex__Ocomplex__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__1) ).
fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
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__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__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_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_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__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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(fact_fz_I1_J,axiom,
c_SEQ_Osubseq(v_f____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fz_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(i_0_1258,plain,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),X6)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_div__if]) ).
fof(i_0_1259,plain,
! [X7,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X7,X6) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6),X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_div__geq]) ).
fof(i_0_1260,plain,
! [X6,X49] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X6) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),X6)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X49)),X6) ) ),
inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of__add]) ).
fof(i_0_1261,plain,
! [X19,X21,X42] :
( epred1_3(X42,X21,X19)
<=> ( ( X21 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ! [X48] :
( ? [X38] :
( 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,X21)
& X19 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X48),X38) )
=> hBOOL(hAPP(X42,X48)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X48] :
( ? [X38] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X38)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& X19 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X48),X38) )
=> hBOOL(hAPP(X42,X48)) ) ) ) ),
introduced(definition) ).
fof(i_0_1262,plain,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Nat_OSuc(X6))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> X7 = c_Nat_OSuc(X6) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_1263,plain,
! [X19,X18] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X18) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_1264,plain,
! [X19,X18] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X19)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X18)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_1265,plain,
! [X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Nat_OSuc(X6))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> X7 = X6 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_1266,plain,
! [X7,X6] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(X7))
=> X7 = X6 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_1267,plain,
! [X18,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X18))
<=> X19 = X18 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_1268,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X6),X6),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_1269,plain,
! [X49] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(X49)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__diff__1]) ).
fof(i_0_1270,plain,
! [X49] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X49)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__1]) ).
fof(i_0_1271,plain,
! [X49] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X49)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of]) ).
fof(i_0_1272,plain,
! [X49] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X49)) ) ),
inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of]) ).
fof(i_0_1273,plain,
! [X2962,X2963,X2964,X2965] :
( ~ class_Orderings_Oorder(X2965)
| ~ c_Orderings_Oord__class_Oless__eq(X2965,hAPP(X2964,esk5_4(X2962,X2963,X2964,X2965)),hAPP(X2964,c_Nat_OSuc(esk5_4(X2962,X2963,X2964,X2965))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2963,X2962)
| c_Orderings_Oord__class_Oless__eq(X2965,hAPP(X2964,X2963),hAPP(X2964,X2962)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__le])])]) ).
fof(i_0_1274,plain,
! [X3641] : c_Nat_OSuc(X3641) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3641,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1275,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(i_0_1276,plain,
! [X5001,X5002,X5003] :
( ~ class_Rings_Ocomm__ring__1(X5003)
| c_Groups_Ominus__class_Ominus(X5003,hAPP(hAPP(c_Power_Opower__class_Opower(X5003),X5002),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5003),X5001),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5003),c_Groups_Ominus__class_Ominus(X5003,X5002,X5001)),c_Groups_Oplus__class_Oplus(X5003,X5002,X5001)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__two__diff])]) ).
fof(i_0_1277,plain,
! [X4791,X4792,X4793] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4793)),X4792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4793)),X4791))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4792,X4791) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4792,X4791)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4793)),X4792),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4793)),X4791)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).
fof(i_0_1278,plain,
! [X4798,X4799,X4800] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4800)),X4799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4800)),X4798))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4799,X4798) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4799,X4798)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4800)),X4799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4800)),X4798)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).
fof(i_0_1279,plain,
! [X5202,X5203] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),esk71_2(X5202,X5203))),X5203),X5202)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5202)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5203) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5202,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk71_2(X5202,X5203)))),X5203))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5202)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5203) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reals__Archimedean4])])])]) ).
fof(i_0_1280,plain,
! [X4958,X4959] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X4959))),X4958)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X4958)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X4959)),X4958))),
inference(variable_rename,[status(thm)],[fact_cis__real__of__nat__Suc__mult]) ).
fof(i_0_1281,plain,
! [X5339] : c_Complex_Ocis(X5339) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5339),
inference(variable_rename,[status(thm)],[fact_cis__rcis__eq]) ).
fof(i_0_1282,plain,
! [X3897,X3898,X3899,X3902,X3903,X3906] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3899)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3898,hAPP(X3897,esk39_3(X3897,X3898,X3899))),X3899)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3898,hAPP(X3897,X3902)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk40_2(X3897,X3898))))
| ~ class_RealVector_Oreal__normed__vector(X3898) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk42_2(X3897,X3898))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3898,hAPP(X3897,esk41_3(X3897,X3898,X3903))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X3903)))
| ~ class_RealVector_Oreal__normed__vector(X3898) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3898,hAPP(X3897,X3906)),esk42_2(X3897,X3898))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3898,hAPP(X3897,esk41_3(X3897,X3898,X3903))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X3903)))
| ~ class_RealVector_Oreal__normed__vector(X3898) ) ),
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_1283,plain,
! [X3887,X3888,X3889,X3892,X3893,X3896] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3889)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3888,hAPP(X3887,esk35_3(X3887,X3888,X3889))),X3889)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3888,hAPP(X3887,X3892)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk36_2(X3887,X3888))))
| ~ class_RealVector_Oreal__normed__vector(X3888) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk38_2(X3887,X3888))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3888,hAPP(X3887,esk37_3(X3887,X3888,X3893))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X3893)))
| ~ class_RealVector_Oreal__normed__vector(X3888) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3888,hAPP(X3887,X3896)),esk38_2(X3887,X3888))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3888,hAPP(X3887,esk37_3(X3887,X3888,X3893))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X3893)))
| ~ class_RealVector_Oreal__normed__vector(X3888) ) ),
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_1284,plain,
! [X4013,X4014,X4016,X4017] :
( ( ~ c_SEQ_OBseq(X4014,X4013)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4014,hAPP(X4013,X4016)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk47_2(X4013,X4014))))
| ~ class_RealVector_Oreal__normed__vector(X4014) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4014,hAPP(X4013,esk48_3(X4013,X4014,X4017))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X4017)))
| c_SEQ_OBseq(X4014,X4013)
| ~ class_RealVector_Oreal__normed__vector(X4014) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Bseq__iff1a])])])])]) ).
fof(i_0_1285,plain,
! [X4019,X4020,X4022,X4023] :
( ( ~ c_SEQ_OBseq(X4020,X4019)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4020,hAPP(X4019,X4022)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk49_2(X4019,X4020))))
| ~ class_RealVector_Oreal__normed__vector(X4020) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4020,hAPP(X4019,esk50_3(X4019,X4020,X4023))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X4023)))
| c_SEQ_OBseq(X4020,X4019)
| ~ class_RealVector_Oreal__normed__vector(X4020) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Bseq__iff])])])])]) ).
fof(i_0_1286,plain,
! [X5122,X5123,X5124,X5125] :
( ~ class_Rings_Olinordered__semidom(X5125)
| ~ c_Orderings_Oord__class_Oless__eq(X5125,hAPP(hAPP(c_Power_Opower__class_Opower(X5125),X5124),c_Nat_OSuc(X5123)),hAPP(hAPP(c_Power_Opower__class_Opower(X5125),X5122),c_Nat_OSuc(X5123)))
| ~ c_Orderings_Oord__class_Oless__eq(X5125,c_Groups_Ozero__class_Ozero(X5125),X5122)
| c_Orderings_Oord__class_Oless__eq(X5125,X5124,X5122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base])]) ).
fof(i_0_1287,plain,
! [X5357,X5358,X5359,X5361,X5362,X5363,X5364] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5357),esk75_3(X5357,X5358,X5359)),X5358)
| X5357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X5359,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5358,X5357))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5357),c_Nat_OSuc(esk75_3(X5357,X5358,X5359))))
| X5357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X5359,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5358,X5357))) )
& ( hBOOL(hAPP(X5359,esk75_3(X5357,X5358,X5359)))
| X5357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X5359,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5358,X5357))) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5357),esk75_3(X5357,X5358,X5359)),X5358)
| hBOOL(hAPP(X5359,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X5359,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5358,X5357))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5357),c_Nat_OSuc(esk75_3(X5357,X5358,X5359))))
| hBOOL(hAPP(X5359,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X5359,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5358,X5357))) )
& ( hBOOL(hAPP(X5359,esk75_3(X5357,X5358,X5359)))
| hBOOL(hAPP(X5359,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X5359,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5358,X5357))) )
& ( X5361 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X5363,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X5363,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5362,X5361))) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5361),X5364),X5362)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5362,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5361),c_Nat_OSuc(X5364)))
| ~ hBOOL(hAPP(X5363,X5364))
| hBOOL(hAPP(X5363,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5362,X5361))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div_H])])])])])]) ).
fof(i_0_1288,plain,
! [X5185,X5186,X5187,X5188] :
( ~ class_Groups_Omonoid__mult(X5188)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5187,X5186)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5188),X5185),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X5186),X5187)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5188),hAPP(hAPP(c_Power_Opower__class_Opower(X5188),X5185),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5186,X5187))),X5185) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__realpow__diff])]) ).
fof(i_0_1289,plain,
! [X5354,X5355,X5356] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5356),X5355),X5354)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5354,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5356),c_Nat_OSuc(X5355)))
| X5355 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5354,X5356)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5356) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5356),X5355),X5354)
| X5355 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5354,X5356)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5356) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5354,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5356),c_Nat_OSuc(X5355)))
| X5355 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5354,X5356)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5356) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div__lemma])])]) ).
fof(i_0_1290,plain,
! [X23,X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X23)),c_Groups_Ozero__class_Ozero(X5)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_1291,plain,
! [X5197,X5198,X5199,X5200,X5201] : hAPP(hAPP(c_Power_Opower_Opower(X5201,X5200,X5199),X5198),c_Nat_OSuc(X5197)) = hAPP(hAPP(X5199,X5198),hAPP(hAPP(c_Power_Opower_Opower(X5201,X5200,X5199),X5198),X5197)),
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(i_0_1292,plain,
! [X4745,X4746,X4747] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4747)),X4746) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4747)),X4745)
| X4746 = X4745 )
& ( X4746 != X4745
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4747)),X4746) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4747)),X4745) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).
fof(i_0_1293,plain,
! [X4811,X4812] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4812)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4811)
| 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),X4811),X4812)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).
fof(i_0_1294,plain,
! [X4819,X4820] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4820)
| ~ 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),X4820),X4819)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4819)
| ~ 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),X4820),X4819)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4820)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4819)
| 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),X4820),X4819)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).
fof(i_0_1295,plain,
! [X3054,X3055] :
( ~ class_Orderings_Oorder(X3055)
| ~ c_Orderings_Oord__class_Oless__eq(X3055,hAPP(X3054,c_Nat_OSuc(esk21_2(X3054,X3055))),hAPP(X3054,esk21_2(X3054,X3055)))
| c_SEQ_Omonoseq(X3055,X3054) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__SucI2])])]) ).
fof(i_0_1296,plain,
! [X3002,X3003,X3004,X3005] :
( ( ~ c_SEQ_Omonoseq(X3003,X3002)
| c_Orderings_Oord__class_Oless__eq(X3003,hAPP(X3002,X3004),hAPP(X3002,c_Nat_OSuc(X3004)))
| c_Orderings_Oord__class_Oless__eq(X3003,hAPP(X3002,c_Nat_OSuc(X3005)),hAPP(X3002,X3005))
| ~ class_Orderings_Oorder(X3003) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3003,hAPP(X3002,esk14_2(X3002,X3003)),hAPP(X3002,c_Nat_OSuc(esk14_2(X3002,X3003))))
| c_SEQ_Omonoseq(X3003,X3002)
| ~ class_Orderings_Oorder(X3003) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3003,hAPP(X3002,c_Nat_OSuc(esk15_2(X3002,X3003))),hAPP(X3002,esk15_2(X3002,X3003)))
| c_SEQ_Omonoseq(X3003,X3002)
| ~ class_Orderings_Oorder(X3003) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monoseq__Suc])])])])]) ).
fof(i_0_1297,plain,
! [X3057,X3058] :
( ~ class_Orderings_Oorder(X3058)
| ~ c_Orderings_Oord__class_Oless__eq(X3058,hAPP(X3057,esk22_2(X3057,X3058)),hAPP(X3057,c_Nat_OSuc(esk22_2(X3057,X3058))))
| c_SEQ_Omonoseq(X3058,X3057) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__SucI1])])]) ).
fof(i_0_1298,plain,
! [X3039,X3040] :
( ~ class_Orderings_Oorder(X3040)
| ~ c_Orderings_Oord__class_Oless__eq(X3040,hAPP(X3039,esk16_2(X3039,X3040)),hAPP(X3039,c_Nat_OSuc(esk16_2(X3039,X3040))))
| c_SEQ_Oincseq(X3040,X3039) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incseq__SucI])])]) ).
fof(i_0_1299,plain,
! [X15,X68,X49] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)),X15)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)),X15)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X68))),X15) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left]) ).
fof(i_0_1300,plain,
! [X3064,X3065,X3066] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3066,X3065)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3065,X3066)),X3064) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3065),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3066,X3064)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])]) ).
fof(i_0_1301,plain,
! [X3650,X3651,X3652] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3652,X3651)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3650,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3651,X3652))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3650,X3652),c_Nat_OSuc(X3651)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1])]) ).
fof(i_0_1302,plain,
! [X5118,X5119,X5120,X5121] :
( ~ class_Rings_Olinordered__semidom(X5121)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5121),X5120),c_Nat_OSuc(X5119)) != hAPP(hAPP(c_Power_Opower__class_Opower(X5121),X5118),c_Nat_OSuc(X5119))
| ~ c_Orderings_Oord__class_Oless__eq(X5121,c_Groups_Ozero__class_Ozero(X5121),X5120)
| ~ c_Orderings_Oord__class_Oless__eq(X5121,c_Groups_Ozero__class_Ozero(X5121),X5118)
| X5120 = X5118 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).
fof(i_0_1303,plain,
! [X5205,X5206] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5206)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5205)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5205),X5206),X5205) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5205),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5206,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_1304,plain,
! [X3654] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3654,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X3654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3654 = 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_1305,plain,
! [X8,X10,X42] :
( hBOOL(hAPP(X42,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X8)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X8)
& ~ hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X44] :
( X10 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X44)
& ~ hBOOL(hAPP(X42,X44)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(i_0_1306,plain,
! [X4809,X4810] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4810)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4809)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4810),X4809)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).
fof(i_0_1307,plain,
! [X4807,X4808] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4808)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4807)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4808,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4807),X4808)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).
fof(i_0_1308,plain,
! [X3408,X3409,X3410] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3410),X3409),c_Nat_OSuc(X3408)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3410,X3409),X3408),
inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).
fof(i_0_1309,plain,
! [X3060,X3061,X3062,X3063] :
( ~ class_Rings_Osemiring__1(X3063)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3063,X3062,c_Nat_OSuc(X3061),X3060) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3063,X3062,X3061,hAPP(X3062,X3060)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])]) ).
fof(i_0_1310,plain,
! [X92,X23,X93,X94] :
( X94 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X93),X23),X92)
=> ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X93)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X92)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X92,X93) ) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X93)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X93,X92)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X92,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
=> ( X93 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X94,X93) = X23 ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq]) ).
fof(i_0_1311,plain,
! [X5365,X5366] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5366)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5366,X5365)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5365,X5366) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5365,X5366),X5366)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__div__geq])]) ).
fof(i_0_1312,plain,
! [X5159,X5160,X5161] :
( ~ class_Rings_Olinordered__semidom(X5161)
| ~ c_Orderings_Oord__class_Oless(X5161,c_Groups_Ozero__class_Ozero(X5161),X5160)
| ~ c_Orderings_Oord__class_Oless(X5161,X5160,c_Groups_Oone__class_Oone(X5161))
| c_Orderings_Oord__class_Oless(X5161,hAPP(hAPP(c_Power_Opower__class_Opower(X5161),X5160),c_Nat_OSuc(X5159)),c_Groups_Oone__class_Oone(X5161)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).
fof(i_0_1313,plain,
! [X4996,X4997,X4998] :
( ~ class_Rings_Olinordered__semidom(X4998)
| ~ c_Orderings_Oord__class_Oless__eq(X4998,c_Groups_Ozero__class_Ozero(X4998),X4997)
| ~ c_Orderings_Oord__class_Oless__eq(X4998,X4997,c_Groups_Oone__class_Oone(X4998))
| c_Orderings_Oord__class_Oless__eq(X4998,hAPP(hAPP(c_Power_Opower__class_Opower(X4998),X4997),c_Nat_OSuc(X4996)),X4997) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__Suc__le__self])]) ).
fof(i_0_1314,plain,
! [X3646,X3647,X3648] :
( ( ~ c_SEQ_Osubseq(X3646)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3646,X3647),hAPP(X3646,c_Nat_OSuc(X3647))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3648,esk30_1(X3648)),hAPP(X3648,c_Nat_OSuc(esk30_1(X3648))))
| c_SEQ_Osubseq(X3648) ) ),
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_subseq__Suc__iff])])])])]) ).
fof(i_0_1315,plain,
! [X15,X68,X49] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68),X15)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68),X15) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X68))
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68),X15)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),X15) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X68))
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68),X15)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X68)),X15) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__left]) ).
fof(i_0_1316,plain,
! [X4072,X4073] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4073)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4072),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4073)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4072,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(X4073))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of])]) ).
fof(i_0_1317,plain,
! [X4077] : c_Int_Opred(X4077) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4077,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_pred__def]) ).
fof(i_0_1318,plain,
! [X5340,X5341] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5340,X5341)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5340,X5341) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5341) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5340,X5341)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5340,X5341) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5340,X5341),X5341))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5341) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1258])])]) ).
fof(i_0_1319,plain,
! [X5342,X5343] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5343)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5342,X5343)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5342,X5343) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5342,X5343),X5343)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1259])]) ).
fof(i_0_1320,plain,
! [X4638,X4639,X4641,X4642,X4643] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4639,X4638)
| X4638 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4639,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(esk60_2(X4638,X4639)))) )
& ( X4641 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4642,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X4643)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4642,X4641) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__iff__Suc__zadd])])])])]) ).
fof(i_0_1321,plain,
! [X3997,X3998] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3998))
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3998),X3997)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3997) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3998))
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3998),X3997)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X3998)),X3997) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1260])]) ).
fof(i_0_1322,plain,
! [X4008] : c_Int_Osucc(X4008) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4008,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_succ__def]) ).
fof(i_0_1323,plain,
! [X5020,X5021] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5021)
| 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),X5021),X5020)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).
fof(i_0_1324,plain,
! [X5137,X5138,X5139] :
( ~ class_Rings_Olinordered__semidom(X5139)
| ~ c_Orderings_Oord__class_Oless(X5139,c_Groups_Oone__class_Oone(X5139),X5138)
| c_Orderings_Oord__class_Oless(X5139,c_Groups_Oone__class_Oone(X5139),hAPP(hAPP(c_Power_Opower__class_Opower(X5139),X5138),c_Nat_OSuc(X5137))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).
fof(i_0_1325,plain,
! [X3464,X3465] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3465),c_Nat_OSuc(X3464))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3465,X3464) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_1326,plain,
! [X3447,X3448] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3448),c_Nat_OSuc(X3447))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3448,X3447) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3448,X3447)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3448),c_Nat_OSuc(X3447)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_1327,plain,
! [X2797,X2798] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2798),c_Nat_OSuc(X2797))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2798,X2797) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2798,X2797)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2798),c_Nat_OSuc(X2797)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_1328,plain,
! [X3146] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3146)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3146,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X3146 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).
fof(i_0_1329,plain,
! [X3147,X3148] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3148)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3148,c_Nat_OSuc(X3147)),X3148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).
fof(i_0_1330,plain,
! [X19,X42] :
( ~ hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X42,X19))
=> ? [X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X19)
& ! [X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X22)
=> ~ hBOOL(hAPP(X42,X48)) )
& hBOOL(hAPP(X42,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).
fof(i_0_1331,plain,
! [X3277,X3278] :
( ( X3278 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3278,X3277) = X3277 )
& ( X3278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3278,X3277) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3278,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3277)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).
fof(i_0_1332,axiom,
! [X21,X19,X42] :
( hBOOL(hAPP(X42,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X19,X21)))
<=> epred1_3(X42,X21,X19) ),
inference(apply_def,[status(thm)],[fact_split__zdiv,c_0_1261]) ).
fof(i_0_1333,plain,
! [X4974,X4975,X4976] :
( ~ class_Rings_Ocomm__semiring__1(X4976)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4976),hAPP(hAPP(c_Power_Opower__class_Opower(X4976),X4975),X4974)),X4975) = hAPP(hAPP(c_Power_Opower__class_Opower(X4976),X4975),c_Nat_OSuc(X4974)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).
fof(i_0_1334,plain,
! [X5105,X5106,X5107] :
( ~ class_Groups_Omonoid__mult(X5107)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5107),X5106),c_Nat_OSuc(X5105)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5107),hAPP(hAPP(c_Power_Opower__class_Opower(X5107),X5106),X5105)),X5106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).
fof(i_0_1335,plain,
! [X3817] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),esk34_1(X3817)),X3817)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3817) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3817,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk34_1(X3817))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3817) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6a])])])]) ).
fof(i_0_1336,plain,
! [X4796,X4797] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X4797)),X4796) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4796,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4797),X4796)),
inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).
fof(i_0_1337,plain,
! [X3562,X3563] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3563,X3562)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3562),X3563) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3562,X3563)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).
fof(i_0_1338,plain,
! [X4078] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X4078)))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4078) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4078) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X4078))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0])]) ).
fof(i_0_1339,plain,
! [X3595,X3596] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3596,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3596,X3595))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_1340,plain,
! [X3597,X3598] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3598,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3597,X3598))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_1341,plain,
! [X2799,X2800] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2800,c_Nat_OSuc(X2799))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2800,X2799)
| X2800 = c_Nat_OSuc(X2799) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2800,X2799)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2800,c_Nat_OSuc(X2799)) )
& ( X2800 != c_Nat_OSuc(X2799)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2800,c_Nat_OSuc(X2799)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_1342,plain,
! [X2793,X2794] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2794,c_Nat_OSuc(X2793))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2794,X2793)
| X2794 = c_Nat_OSuc(X2793) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1262])]) ).
fof(i_0_1343,plain,
! [X3069,X3070] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3070,X3069)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3070),c_Nat_OSuc(X3069)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_1344,plain,
! [X4,X6] :
( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X6))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X6))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_natfloor__add__number__of]) ).
fof(i_0_1345,plain,
! [X4,X6] :
( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X6))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X6))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_natceiling__add__number__of]) ).
fof(i_0_1346,plain,
! [X51,X53,X5] :
( ( class_Int_Onumber(X5)
& class_Orderings_Olinorder(X5) )
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Int_Onumber__class_Onumber__of(X5,X53),c_Int_Onumber__class_Onumber__of(X5,X51))
<=> ~ c_Orderings_Oord__class_Oless(X5,c_Int_Onumber__class_Onumber__of(X5,X51),c_Int_Onumber__class_Onumber__of(X5,X53)) ) ),
inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).
fof(i_0_1347,plain,
! [X3702] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3702))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3702) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3702),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_expand__Suc])]) ).
fof(i_0_1348,plain,
! [X5050,X5051] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X5051)),X5050) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5050)),X5051)),
inference(variable_rename,[status(thm)],[fact_DeMoivre]) ).
fof(i_0_1349,plain,
! [X3089,X3090,X3092,X3093,X3094] :
( ( X3090 = c_Nat_OSuc(esk24_2(X3089,X3090))
| X3090 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3090,c_Nat_OSuc(X3089)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk24_2(X3089,X3090),X3089)
| X3090 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3090,c_Nat_OSuc(X3089)) )
& ( X3093 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3093,c_Nat_OSuc(X3092)) )
& ( X3093 != c_Nat_OSuc(X3094)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3094,X3092)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3093,c_Nat_OSuc(X3092)) ) ),
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_1350,plain,
! [X3607,X3608] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3607,c_Nat_OSuc(X3608))
| X3607 = X3608
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3608,X3607) )
& ( X3607 != X3608
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3607,c_Nat_OSuc(X3608))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3608,X3607) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_1351,plain,
! [X2801,X2802] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2802,X2801)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2801),X2802) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2801),X2802)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2802,X2801) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1263])]) ).
fof(i_0_1352,plain,
! [X3443,X3444] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3444,X3443)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3443,c_Nat_OSuc(X3444)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3443,c_Nat_OSuc(X3444))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3444,X3443) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1264])]) ).
fof(i_0_1353,plain,
! [X5031] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5031) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).
fof(i_0_1354,plain,
! [X3457,X3458,X3459] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3459,X3458)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3458,X3457)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3459),X3457) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_1355,plain,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X4),
inference(fof_simplification,[status(thm)],[fact_abs__add__one__not__less__self]) ).
fof(i_0_1356,plain,
! [X3406,X3407] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3407),c_Nat_OSuc(X3406)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3407,X3406),
inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).
fof(i_0_1357,plain,
! [X2750,X2751] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X2751),X2750) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2751,c_Nat_OSuc(X2750)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_1358,plain,
! [X3074,X3075] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3075,c_Nat_OSuc(X3074)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3075,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3074),
inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).
fof(i_0_1359,plain,
! [X5102,X5103,X5104] :
( ~ class_Power_Opower(X5104)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5104),X5103),c_Nat_OSuc(X5102)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5104),X5103),hAPP(hAPP(c_Power_Opower__class_Opower(X5104),X5103),X5102)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).
fof(i_0_1360,plain,
! [X4980,X4981,X4982] :
( ~ class_Rings_Ocomm__semiring__1(X4982)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4982),X4981),c_Nat_OSuc(X4980)) = 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_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).
fof(i_0_1361,plain,
! [X4977,X4978,X4979] :
( ~ class_Rings_Ocomm__semiring__1(X4979)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4979),X4978),hAPP(hAPP(c_Power_Opower__class_Opower(X4979),X4978),X4977)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4979),X4978),c_Nat_OSuc(X4977)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).
fof(i_0_1362,plain,
! [X2748,X2749] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X2749),X2748) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2749,X2748)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_1363,plain,
! [X2746,X2747] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2747,c_Nat_OSuc(X2746)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2747,X2746)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_1364,plain,
! [X24,X19] :
( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X19))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X19),c_RComplete_Onatfloor(X24))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X19),X24) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__natfloor__eq__number__of]) ).
fof(i_0_1365,plain,
! [X24,X19] :
( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X19))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X24),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X19)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_natceiling__le__eq__number__of]) ).
fof(i_0_1366,plain,
! [X68,X49] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X68)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).
fof(i_0_1367,plain,
! [X3460,X3461] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3461,c_Nat_OSuc(X3460))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3461,X3460)
| X3461 = X3460 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1265])]) ).
fof(i_0_1368,plain,
! [X3451,X3452] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3452,X3451)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3452,c_Nat_OSuc(X3451))
| X3451 = X3452 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1266])]) ).
fof(i_0_1369,plain,
! [X3449,X3450] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3450,c_Nat_OSuc(X3449))
| X3450 = X3449
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3450,X3449) )
& ( X3450 != X3449
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3450,c_Nat_OSuc(X3449))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3450,X3449) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1267])])]) ).
fof(i_0_1370,plain,
! [X3445,X3446] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3446,c_Nat_OSuc(X3445))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3446,X3445)
| X3446 = X3445 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3446,X3445)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3446,c_Nat_OSuc(X3445)) )
& ( X3446 != X3445
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3446,c_Nat_OSuc(X3445)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_1371,plain,
! [X3462,X3463] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3463),X3462)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3463,X3462) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_1372,plain,
! [X3617,X3618] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3618,X3617)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3618),X3617) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3618),X3617)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3618,X3617) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_1373,plain,
! [X3613,X3614] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3614),X3613)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3614,X3613) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3614,X3613)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3614),X3613) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_1374,plain,
! [X3605,X3606] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3606),X3605)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3606,X3605) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_1375,plain,
! [X4075,X4076] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4076,X4075)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X4076),X4075) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X4076),X4075)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4076,X4075) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])]) ).
fof(i_0_1376,plain,
! [X2791,X2792] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2792),X2791)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2792,X2791) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_1377,plain,
! [X3615,X3616] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3616,c_Nat_OSuc(X3615))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3616,X3615) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3616,X3615)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3616,c_Nat_OSuc(X3615)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_1378,plain,
! [X3682] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X3682))),
inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc__gt__zero]) ).
fof(i_0_1379,plain,
! [X3599,X3600,X3602,X3603,X3604] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3600,X3599)
| X3599 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3600,esk29_2(X3599,X3600))) )
& ( X3602 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3603,X3604))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3603,X3602) ) ),
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_1380,plain,
! [X3455,X3456] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3456,X3455)
| c_Nat_OSuc(X3456) = X3455
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3456),X3455) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_1381,plain,
! [X6,X15,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X15),X6)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_1382,plain,
! [X4794,X4795] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4795),c_Nat_OSuc(X4794)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4795,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4795),X4794)),
inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).
fof(i_0_1383,plain,
! [X3642,X3643] :
( ( X3643 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3643 = 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,X3643,X3642) )
& ( X3642 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3643 = 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,X3643,X3642) )
& ( X3643 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3642 = 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,X3643,X3642) )
& ( X3642 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3642 = 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,X3643,X3642) )
& ( X3643 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3642 != 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,X3643,X3642) )
& ( X3643 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3642 != 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,X3643,X3642) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_1384,plain,
! [X3644,X3645] :
( ( X3645 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3645 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3645,X3644) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3644 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3645 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3645,X3644) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3645 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3645,X3644) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3644 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3645,X3644) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3645 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3644 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3645,X3644) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3645 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3644 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3645,X3644) = 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_1385,plain,
! [X1,X2,X5,X25] :
( class_Orderings_Oord(X25)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X5,X25),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X25),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X25),X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_1386,plain,
! [X4767,X4768] :
( ( X4768 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4768),X4767) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4767 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4768),X4767) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4768 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4767 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4768),X4767) = 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_1387,plain,
! [X3088] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3088,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3088 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3088 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3088,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_1388,plain,
! [X68,X49] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Int_OPls)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X68)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X68)) ) ),
inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of]) ).
fof(i_0_1389,plain,
! [X3252,X3253] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3253,X3252),c_Nat_OSuc(X3253)),
inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).
fof(i_0_1390,plain,
! [X13,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X13),X13),c_Groups_Ozero__class_Ozero(X5)) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_1391,plain,
! [X4994,X4995] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X4995)),c_Complex_Ocis(X4994)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4995,X4994)),
inference(variable_rename,[status(thm)],[fact_cis__mult]) ).
fof(i_0_1392,plain,
! [X67,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X53),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X67))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X67)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,c_Int_OPls) ) ),
inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).
fof(i_0_1393,plain,
! [X2803] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2803),X2803),
inference(variable_rename,[status(thm)],[i_0_1268]) ).
fof(i_0_1394,plain,
! [X3076] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3076)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3076,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X3076 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).
fof(i_0_1395,plain,
! [X3077] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3077)
| X3077 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3077,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_1396,plain,
! [X4071] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4071,c_Int_OPls)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4071),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4071,c_Int_OPls)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4071),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(X4071)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1269])]) ).
fof(i_0_1397,plain,
! [X4044] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4044,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4044),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4044,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4044),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X4044)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1270])]) ).
fof(i_0_1398,plain,
! [X4043] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4043,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4043)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4043,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4043)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X4043)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1271])]) ).
fof(i_0_1399,plain,
! [X3609,X3610] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3610,X3609)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3610),X3609) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_1400,plain,
! [X3453,X3454] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3454,X3453)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3454,c_Nat_OSuc(X3453)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_1401,plain,
! [X3611,X3612] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3612,X3611)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3612,c_Nat_OSuc(X3611)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_1402,plain,
! [X2795,X2796] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2796,X2795)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2796,c_Nat_OSuc(X2795)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_1403,plain,
! [X16,X17] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X16),X17),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_1404,plain,
! [X17,X16] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X17),X17),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_1405,plain,
! [X24] :
( ~ 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),X24),X24))
<=> X24 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(i_0_1406,plain,
! [X4538,X4539] :
( ~ class_Rings_Osemiring__1(X4539)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4539),c_Nat_OSuc(X4538)) = c_Groups_Oplus__class_Oplus(X4539,c_Groups_Oone__class_Oone(X4539),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4539),X4538)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__Suc])]) ).
fof(i_0_1407,plain,
! [X5032,X5033] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5033),X5032) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X5032 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X5033 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X5032 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5033),X5032) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X5033 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5033),X5032) = 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_1408,plain,
! [X3999] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3999))
| c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3999)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3999))
| c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3999)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X3999)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1272])]) ).
fof(i_0_1409,plain,
! [X4009,X4010] :
( ~ class_Int_Onumber__ring(X4010)
| c_Int_Onumber__class_Onumber__of(X4010,c_Int_Osucc(X4009)) = c_Groups_Oplus__class_Oplus(X4010,c_Groups_Oone__class_Oone(X4010),c_Int_Onumber__class_Onumber__of(X4010,X4009)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__succ])]) ).
fof(i_0_1410,plain,
! [X67,X53] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X53) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X67)
<=> ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X53))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X67),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X53))
=> ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X67))
=> c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X53) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X67))
=> X53 = X67 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_eq__nat__number__of]) ).
fof(i_0_1411,plain,
! [X3008] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X3008)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3008),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc]) ).
fof(i_0_1412,plain,
! [X4644] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X4644)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4644)),
inference(variable_rename,[status(thm)],[fact_int__Suc]) ).
fof(i_0_1413,plain,
! [X6,X7] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X6)) = X7 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(i_0_1414,plain,
! [X27,X24,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
& ~ c_Orderings_Oord__class_Oless__eq(X5,X27,X24) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_1415,plain,
! [X5100,X5101] :
( ~ class_Power_Opower(X5101)
| ~ class_Rings_Osemiring__0(X5101)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5101),c_Groups_Ozero__class_Ozero(X5101)),c_Nat_OSuc(X5100)) = c_Groups_Ozero__class_Ozero(X5101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).
fof(i_0_1416,plain,
! [X49,X5] :
( class_Int_Onumber__ring(X5)
=> ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(X5,X49) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__lemma]) ).
fof(i_0_1417,plain,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> X24 = X27 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_1418,plain,
! [X13,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X13)
=> ~ c_Orderings_Oord__class_Oless(X5,X13,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_1419,plain,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> ( c_Orderings_Oord__class_Oless(X5,X27,X24)
| X24 = X27 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_1420,plain,
! [X4,X23,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X23,X4)
=> ~ c_Orderings_Oord__class_Oless(X5,X4,X23) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_1421,plain,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> c_Orderings_Oord__class_Oless__eq(X5,X27,X24) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_1422,plain,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
<=> c_Orderings_Oord__class_Oless(X5,X27,X24) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_1423,plain,
! [X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> ~ c_Orderings_Oord__class_Oless(X5,X23,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_1424,plain,
! [X12,X13,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ~ c_Orderings_Oord__class_Oless(X5,X12,X13) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_1425,plain,
! [X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> ~ c_Orderings_Oord__class_Oless(X5,X23,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_1426,plain,
! [X23,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X23)
=> ~ c_Orderings_Oord__class_Oless(X5,X23,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_1427,plain,
! [X2926,X2927] :
( ( c_Nat_OSuc(X2927) != c_Nat_OSuc(X2926)
| X2927 = X2926 )
& ( X2927 != X2926
| c_Nat_OSuc(X2927) = c_Nat_OSuc(X2926) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1428,plain,
! [X2924,X2925] :
( c_Nat_OSuc(X2925) != c_Nat_OSuc(X2924)
| X2925 = X2924 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1429,plain,
! [X5314] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5314,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X5314,
inference(variable_rename,[status(thm)],[fact_div__1]) ).
fof(i_0_1430,plain,
! [X3073] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3073),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3073,
inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).
fof(i_0_1431,plain,
! [X4074] : c_Int_Osucc(c_Int_Opred(X4074)) = X4074,
inference(variable_rename,[status(thm)],[fact_succ__pred]) ).
fof(i_0_1432,plain,
! [X3072] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X3072)),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_1433,plain,
! [X3068] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3068,c_Nat_OSuc(X3068)),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_1434,plain,
! [X7,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X7),c_Groups_Ozero__class_Ozero(X5)) ),
inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff]) ).
fof(i_0_1435,plain,
! [X3084,X3086,X3087] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3084)
| X3084 = c_Nat_OSuc(esk23_1(X3084)) )
& ( X3086 != c_Nat_OSuc(X3087)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3086) ) ),
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_1436,plain,
! [X4,X23] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X4)
=> c_Nat__Transfer_Otsub(X4,X23) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,X23) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,X4)
=> c_Nat__Transfer_Otsub(X4,X23) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).
fof(i_0_1437,plain,
! [X27,X24,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X24,X27)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X24,X27)
<=> X24 = X27 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_1438,plain,
! [X13,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oabs__class_Oabs(X5,X13),c_Groups_Ozero__class_Ozero(X5)) ),
inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).
fof(i_0_1439,plain,
! [X15] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_simplification,[status(thm)],[fact_int__less__0__conv]) ).
fof(i_0_1440,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_simplification,[status(thm)],[fact_not__real__of__nat__less__zero]) ).
fof(i_0_1441,plain,
! [X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero]) ).
fof(i_0_1442,plain,
! [X23,X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X4 != X23
=> ( ~ c_Orderings_Oord__class_Oless(X5,X4,X23)
=> c_Orderings_Oord__class_Oless(X5,X23,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_1443,plain,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X4,X23)
=> ( X4 != X23
=> c_Orderings_Oord__class_Oless(X5,X23,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_1444,plain,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( X4 != X23
=> ( ~ c_Orderings_Oord__class_Oless(X5,X4,X23)
=> c_Orderings_Oord__class_Oless(X5,X23,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_1445,plain,
! [X24,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X24)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X24,X27)
<=> X24 = X27 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_1446,plain,
! [X4,X23,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X23,X4)
=> c_Orderings_Oord__class_Oless(X5,X4,X23) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_1447,plain,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X4,X23)
=> c_Orderings_Oord__class_Oless__eq(X5,X23,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_1448,plain,
! [X23,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X4,X23)
=> c_Orderings_Oord__class_Oless__eq(X5,X23,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_1449,plain,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(X5)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_1450,plain,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(X5)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_1451,plain,
! [X3640] : c_Nat_OSuc(X3640) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3640),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1452,plain,
! [X23,X4] :
( X4 != X23
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X23)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_1453,plain,
! [X49,X5] :
( class_Int_Onumber__ring(X5)
=> ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Ozero__class_Ozero(X5) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(X5,X49) ) ) ),
inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__eq]) ).
fof(i_0_1454,plain,
! [X24] :
( ~ c_Nat__Numeral_Oneg(X24)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) ),
inference(fof_simplification,[status(thm)],[fact_not__neg__eq__ge__0]) ).
fof(i_0_1455,plain,
! [X4,X5] :
( class_Orderings_Opreorder(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,X4,X4) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_1456,plain,
! [X3537] : c_Nat_OSuc(X3537) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1457,plain,
! [X3535] : c_Nat_OSuc(X3535) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1458,plain,
! [X3534] : c_Nat_OSuc(X3534) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1459,plain,
! [X3536] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X3536),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1460,plain,
! [X3533] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X3533),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1461,plain,
! [X3532] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X3532),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1462,plain,
! [X2928] : c_Nat_OSuc(X2928) != X2928,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1463,plain,
! [X2929] : X2929 != c_Nat_OSuc(X2929),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1464,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_1465,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_1466,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_1467,plain,
! [X49] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49) ) ),
inference(fof_simplification,[status(thm)],[fact_int__nat__number__of]) ).
fof(i_0_1468,plain,
! [X49] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
=> hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X49)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X49) ) ),
inference(fof_simplification,[status(thm)],[fact_real__of__nat__number__of]) ).
fof(i_0_1469,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X6),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_1470,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X6),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_1471,plain,
! [X6] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),
inference(fof_simplification,[status(thm)],[fact_not__neg__int]) ).
fof(i_0_1472,plain,
! [X4000,X4001,X4002,X4003,X4005] :
( ( c_Orderings_Oord__class_Oless__eq(X4002,X4001,esk46_4(X4000,X4001,X4002,X4003))
| ~ c_Orderings_Oord__class_Oless__eq(X4002,X4001,X4005)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4003,hAPP(X4000,X4005)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4003,hAPP(X4000,X4001))))
| ~ class_RealVector_Oreal__normed__vector(X4003)
| ~ class_Orderings_Oord(X4002) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4003,c_Groups_Ominus__class_Ominus(X4003,hAPP(X4000,X4001),hAPP(X4000,esk46_4(X4000,X4001,X4002,X4003)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(X4002,X4001,X4005)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4003,hAPP(X4000,X4005)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4003,hAPP(X4000,X4001))))
| ~ class_RealVector_Oreal__normed__vector(X4003)
| ~ class_Orderings_Oord(X4002) ) ),
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])])])])]) ).
cnf(i_0_1473,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4),hAPP(X2,X3))
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk5_4(X3,X4,X2,X1)),hAPP(X2,c_Nat_OSuc(esk5_4(X3,X4,X2,X1))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1273]) ).
cnf(i_0_1474,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_1274]) ).
fof(i_0_1475,plain,
! [X4079,X4080,X4081] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4081)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4080,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4080,X4079)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4081)),X4079) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])]) ).
fof(i_0_1476,plain,
! [X4082,X4083,X4084] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4084)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4083,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4082,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4082,X4083)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4084))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])]) ).
fof(i_0_1477,plain,
! [X2894,X2895,X2896,X2897,X2898] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2896,X2897),X2895,X2894)
| c_Orderings_Oord__class_Oless__eq(X2897,hAPP(X2895,X2898),hAPP(X2894,X2898))
| ~ class_Orderings_Oord(X2897) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2897,hAPP(X2895,esk3_4(X2894,X2895,X2896,X2897)),hAPP(X2894,esk3_4(X2894,X2895,X2896,X2897)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2896,X2897),X2895,X2894)
| ~ class_Orderings_Oord(X2897) ) ),
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_1478,plain,
! [X4503,X4504,X4505,X4506,X4507] :
( ~ class_RealVector_Oreal__normed__algebra(X4507)
| c_Groups_Ominus__class_Ominus(X4507,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4507),X4506),X4505),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4507),X4504),X4503)) = c_Groups_Oplus__class_Oplus(X4507,c_Groups_Oplus__class_Oplus(X4507,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4507),c_Groups_Ominus__class_Ominus(X4507,X4506,X4504)),c_Groups_Ominus__class_Ominus(X4507,X4505,X4503)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4507),c_Groups_Ominus__class_Ominus(X4507,X4506,X4504)),X4503)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4507),X4504),c_Groups_Ominus__class_Ominus(X4507,X4505,X4503))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod])]) ).
cnf(i_0_1479,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(split_conjunct,[status(thm)],[i_0_1275]) ).
fof(i_0_1480,plain,
! [X4632,X4633,X4634,X4635,X4636,X4637] :
( ( ~ c_Orderings_Oord__class_Oless(X4637,c_Groups_Oplus__class_Oplus(X4637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4637),X4636),X4635),X4634),c_Groups_Oplus__class_Oplus(X4637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4637),X4633),X4635),X4632))
| c_Orderings_Oord__class_Oless(X4637,c_Groups_Oplus__class_Oplus(X4637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4637),c_Groups_Ominus__class_Ominus(X4637,X4636,X4633)),X4635),X4634),X4632)
| ~ class_Rings_Oordered__ring(X4637) )
& ( ~ c_Orderings_Oord__class_Oless(X4637,c_Groups_Oplus__class_Oplus(X4637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4637),c_Groups_Ominus__class_Ominus(X4637,X4636,X4633)),X4635),X4634),X4632)
| c_Orderings_Oord__class_Oless(X4637,c_Groups_Oplus__class_Oplus(X4637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4637),X4636),X4635),X4634),c_Groups_Oplus__class_Oplus(X4637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4637),X4633),X4635),X4632))
| ~ class_Rings_Oordered__ring(X4637) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).
fof(i_0_1481,plain,
! [X4614,X4615,X4616,X4617,X4618,X4619] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4619,c_Groups_Oplus__class_Oplus(X4619,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4619),X4618),X4617),X4616),c_Groups_Oplus__class_Oplus(X4619,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4619),X4615),X4617),X4614))
| c_Orderings_Oord__class_Oless__eq(X4619,c_Groups_Oplus__class_Oplus(X4619,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4619),c_Groups_Ominus__class_Ominus(X4619,X4618,X4615)),X4617),X4616),X4614)
| ~ class_Rings_Oordered__ring(X4619) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4619,c_Groups_Oplus__class_Oplus(X4619,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4619),c_Groups_Ominus__class_Ominus(X4619,X4618,X4615)),X4617),X4616),X4614)
| c_Orderings_Oord__class_Oless__eq(X4619,c_Groups_Oplus__class_Oplus(X4619,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4619),X4618),X4617),X4616),c_Groups_Oplus__class_Oplus(X4619,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4619),X4615),X4617),X4614))
| ~ class_Rings_Oordered__ring(X4619) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).
fof(i_0_1482,plain,
! [X4626,X4627,X4628,X4629,X4630,X4631] :
( ( ~ c_Orderings_Oord__class_Oless(X4631,c_Groups_Oplus__class_Oplus(X4631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4631),X4630),X4629),X4628),c_Groups_Oplus__class_Oplus(X4631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4631),X4627),X4629),X4626))
| c_Orderings_Oord__class_Oless(X4631,X4628,c_Groups_Oplus__class_Oplus(X4631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4631),c_Groups_Ominus__class_Ominus(X4631,X4627,X4630)),X4629),X4626))
| ~ class_Rings_Oordered__ring(X4631) )
& ( ~ c_Orderings_Oord__class_Oless(X4631,X4628,c_Groups_Oplus__class_Oplus(X4631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4631),c_Groups_Ominus__class_Ominus(X4631,X4627,X4630)),X4629),X4626))
| c_Orderings_Oord__class_Oless(X4631,c_Groups_Oplus__class_Oplus(X4631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4631),X4630),X4629),X4628),c_Groups_Oplus__class_Oplus(X4631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4631),X4627),X4629),X4626))
| ~ class_Rings_Oordered__ring(X4631) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).
fof(i_0_1483,plain,
! [X4620,X4621,X4622,X4623,X4624,X4625] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4625,c_Groups_Oplus__class_Oplus(X4625,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4624),X4623),X4622),c_Groups_Oplus__class_Oplus(X4625,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4621),X4623),X4620))
| c_Orderings_Oord__class_Oless__eq(X4625,X4622,c_Groups_Oplus__class_Oplus(X4625,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),c_Groups_Ominus__class_Ominus(X4625,X4621,X4624)),X4623),X4620))
| ~ class_Rings_Oordered__ring(X4625) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4625,X4622,c_Groups_Oplus__class_Oplus(X4625,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),c_Groups_Ominus__class_Ominus(X4625,X4621,X4624)),X4623),X4620))
| c_Orderings_Oord__class_Oless__eq(X4625,c_Groups_Oplus__class_Oplus(X4625,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4624),X4623),X4622),c_Groups_Oplus__class_Oplus(X4625,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4621),X4623),X4620))
| ~ class_Rings_Oordered__ring(X4625) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).
fof(i_0_1484,plain,
! [X4868,X4869,X4870,X4871,X4872] :
( ( ~ 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),X4871),X4870),X4869),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4872),X4870),X4868))
| 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,X4871,X4872)),X4870),X4869),X4868)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4872,X4871) )
& ( ~ 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,X4871,X4872)),X4870),X4869),X4868)
| 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),X4871),X4870),X4869),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4872),X4870),X4868))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4872,X4871) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).
fof(i_0_1485,plain,
! [X4914,X4915,X4916,X4917,X4918] :
( ( ~ 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),X4917),X4916),X4915),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4918),X4916),X4914))
| 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,X4917,X4918)),X4916),X4915),X4914)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4918,X4917) )
& ( ~ 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,X4917,X4918)),X4916),X4915),X4914)
| 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),X4917),X4916),X4915),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4918),X4916),X4914))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4918,X4917) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).
fof(i_0_1486,plain,
! [X4863,X4864,X4865,X4866,X4867] :
( ( ~ 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),X4867),X4865),X4864),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4866),X4865),X4863))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4864,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,X4866,X4867)),X4865),X4863))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4867,X4866) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4864,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,X4866,X4867)),X4865),X4863))
| 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),X4867),X4865),X4864),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4866),X4865),X4863))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4867,X4866) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).
fof(i_0_1487,plain,
! [X4899,X4900,X4901,X4902,X4903] :
( ( ~ 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),X4903),X4901),X4900),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4902),X4901),X4899))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4900,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,X4902,X4903)),X4901),X4899))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4903,X4902) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4900,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,X4902,X4903)),X4901),X4899))
| 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),X4903),X4901),X4900),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4902),X4901),X4899))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4903,X4902) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).
fof(i_0_1488,plain,
! [X3798,X3799,X3800,X3801,X3802] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3802)
| c_Orderings_Oord__class_Oless__eq(X3802,c_Groups_Oabs__class_Oabs(X3802,c_Groups_Ominus__class_Ominus(X3802,c_Groups_Oplus__class_Oplus(X3802,X3801,X3800),c_Groups_Oplus__class_Oplus(X3802,X3799,X3798))),c_Groups_Oplus__class_Oplus(X3802,c_Groups_Oabs__class_Oabs(X3802,c_Groups_Ominus__class_Ominus(X3802,X3801,X3799)),c_Groups_Oabs__class_Oabs(X3802,c_Groups_Ominus__class_Ominus(X3802,X3800,X3798)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).
fof(i_0_1489,plain,
! [X5189,X5190] :
( X5190 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X5189 = 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),X5190),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk70_2(X5189,X5190)),X5189)))),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_1490,plain,
! [X3925,X3926,X3927,X3928,X3929] :
( ~ class_RealVector_Oreal__normed__vector(X3929)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3929,c_Groups_Ominus__class_Ominus(X3929,c_Groups_Oplus__class_Oplus(X3929,X3928,X3927),c_Groups_Oplus__class_Oplus(X3929,X3926,X3925))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3929,c_Groups_Ominus__class_Ominus(X3929,X3928,X3926)),c_RealVector_Onorm__class_Onorm(X3929,c_Groups_Ominus__class_Ominus(X3929,X3927,X3925)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__triangle__ineq])]) ).
cnf(i_0_1491,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_1276]) ).
fof(i_0_1492,plain,
! [X4909,X4910,X4911,X4912,X4913] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4913,X4912)
| 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),X4912),X4911),X4910),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4913),X4911),X4909)) = 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,X4912,X4913)),X4911),X4910),X4909) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).
fof(i_0_1493,plain,
! [X4894,X4895,X4896,X4897,X4898] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4898,X4897)
| 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),X4898),X4896),X4895),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4897),X4896),X4894)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4895,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,X4897,X4898)),X4896),X4894)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).
fof(i_0_1494,plain,
! [X4932,X4933,X4934,X4936] :
( ( hBOOL(hAPP(X4933,esk64_3(X4932,X4933,X4934)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4932)
| ~ hBOOL(hAPP(X4933,X4936))
| hBOOL(hAPP(X4933,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4936,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4932),X4934))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4934) )
& ( ~ hBOOL(hAPP(X4933,c_Groups_Ominus__class_Ominus(tc_Int_Oint,esk64_3(X4932,X4933,X4934),X4934)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4932)
| ~ hBOOL(hAPP(X4933,X4936))
| hBOOL(hAPP(X4933,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4936,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4932),X4934))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4934) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__mult__lemma])])])])]) ).
fof(i_0_1495,plain,
! [X4937,X4938,X4939,X4941] :
( ( hBOOL(hAPP(X4938,esk65_3(X4937,X4938,X4939)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4937)
| ~ hBOOL(hAPP(X4938,X4941))
| hBOOL(hAPP(X4938,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4941,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4937),X4939))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4939) )
& ( ~ hBOOL(hAPP(X4938,c_Groups_Oplus__class_Oplus(tc_Int_Oint,esk65_3(X4937,X4938,X4939),X4939)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4937)
| ~ hBOOL(hAPP(X4938,X4941))
| hBOOL(hAPP(X4938,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4941,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4937),X4939))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4939) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma])])])])]) ).
cnf(i_0_1496,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_1277]) ).
cnf(i_0_1497,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_1278]) ).
cnf(i_0_1498,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk71_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_1279]) ).
cnf(i_0_1499,plain,
c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X1))),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X2)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)),X2))),
inference(split_conjunct,[status(thm)],[i_0_1280]) ).
cnf(i_0_1500,plain,
c_Complex_Ocis(X1) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),
inference(split_conjunct,[status(thm)],[i_0_1281]) ).
cnf(i_0_1501,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk40_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,esk39_3(X3,X2,X1))),X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1282]) ).
cnf(i_0_1502,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk36_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,esk35_3(X3,X2,X1))),X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1283]) ).
cnf(i_0_1503,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk42_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk41_3(X2,X1,X4))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X4)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1282]) ).
cnf(i_0_1504,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk38_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk37_3(X2,X1,X4))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X4)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1283]) ).
fof(i_0_1505,plain,
! [X4684,X4685,X4686,X4687,X4688,X4689] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4689),X4688),X4687) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4686),X4685),X4684)
| ~ 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),X4686),X4685),X4684),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4687,X4689)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4684)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4686)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4686,X4689)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4685,X4688) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).
fof(i_0_1506,plain,
! [X4852,X4853,X4854,X4855,X4856,X4857] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4857),X4856),X4855) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4854),X4853),X4852)
| ~ 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),X4854),X4853),X4852))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4852,X4854)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4855)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4854)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4854,X4857)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4856,X4853) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).
fof(i_0_1507,plain,
! [X4675,X4676,X4677] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4675,X4676)
| hBOOL(hAPP(X4677,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4676),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4675))))
| ~ hBOOL(hAPP(X4677,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4676,X4675)))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4676,X4675)
| hBOOL(hAPP(X4677,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X4677,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4676,X4675)))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4676,X4675)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4675,X4676)
| hBOOL(hAPP(X4677,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4676,X4675)))) )
& ( ~ hBOOL(hAPP(X4677,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4675,X4676)
| hBOOL(hAPP(X4677,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4676,X4675)))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4676,X4675)
| ~ hBOOL(hAPP(X4677,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4676),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4675))))
| hBOOL(hAPP(X4677,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4676,X4675)))) )
& ( ~ hBOOL(hAPP(X4677,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X4677,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4676),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4675))))
| hBOOL(hAPP(X4677,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4676,X4675)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int__split])])]) ).
fof(i_0_1508,plain,
! [X4944,X4946,X4947] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk67_1(X4944))
| ~ class_RealVector_Oreal__normed__algebra(X4944) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4944,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4944),X4946),X4947)),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(X4944,X4946)),c_RealVector_Onorm__class_Onorm(X4944,X4947))),esk67_1(X4944)))
| ~ class_RealVector_Oreal__normed__algebra(X4944) ) ),
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])])])])]) ).
fof(i_0_1509,plain,
! [X4924,X4926,X4927] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk62_1(X4924))
| ~ class_RealVector_Oreal__normed__algebra(X4924) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4924,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4924),X4926),X4927)),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(X4924,X4926)),c_RealVector_Onorm__class_Onorm(X4924,X4927))),esk62_1(X4924)))
| ~ class_RealVector_Oreal__normed__algebra(X4924) ) ),
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])])])])]) ).
cnf(i_0_1510,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk42_2(X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk41_3(X1,X2,X3))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X3)))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1282]) ).
cnf(i_0_1511,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk38_2(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk37_3(X1,X2,X3))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X3)))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1283]) ).
cnf(i_0_1512,plain,
( c_SEQ_OBseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk48_3(X2,X1,X3))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1284]) ).
cnf(i_0_1513,plain,
( c_SEQ_OBseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk50_3(X2,X1,X3))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1285]) ).
fof(i_0_1514,plain,
! [X4847,X4848,X4849,X4850,X4851] :
( ~ 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),X4851),X4850),X4849),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4851),X4848),X4847))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4849)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4849,X4851)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4847,X4851)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4850,X4848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).
fof(i_0_1515,plain,
! [X4858,X4859,X4860,X4861,X4862] :
( ~ 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),X4862),X4861),X4860),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4862),X4859),X4858))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4858,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4862,X4858)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4862,X4860)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4859,X4861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).
cnf(i_0_1516,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_1286]) ).
fof(i_0_1517,plain,
! [X4904,X4905,X4906,X4907,X4908] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4907),X4906),X4905) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4908),X4906),X4904)
| 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,X4907,X4908)),X4906),X4905) = X4904
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4908,X4907) )
& ( 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,X4907,X4908)),X4906),X4905) != X4904
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4907),X4906),X4905) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4908),X4906),X4904)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4908,X4907) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).
fof(i_0_1518,plain,
! [X4889,X4890,X4891,X4892,X4893] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4893),X4891),X4890) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4892),X4891),X4889)
| X4890 = 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,X4892,X4893)),X4891),X4889)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4893,X4892) )
& ( X4890 != 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,X4892,X4893)),X4891),X4889)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4893),X4891),X4890) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4892),X4891),X4889)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4893,X4892) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).
fof(i_0_1519,plain,
! [X4492,X4493,X4494,X4495,X4496,X4497] :
( ( c_Groups_Oplus__class_Oplus(X4497,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4497),X4496),X4495),X4494) != c_Groups_Oplus__class_Oplus(X4497,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4497),X4493),X4495),X4492)
| c_Groups_Oplus__class_Oplus(X4497,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4497),c_Groups_Ominus__class_Ominus(X4497,X4496,X4493)),X4495),X4494) = X4492
| ~ class_Rings_Oring(X4497) )
& ( c_Groups_Oplus__class_Oplus(X4497,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4497),c_Groups_Ominus__class_Ominus(X4497,X4496,X4493)),X4495),X4494) != X4492
| c_Groups_Oplus__class_Oplus(X4497,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4497),X4496),X4495),X4494) = c_Groups_Oplus__class_Oplus(X4497,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4497),X4493),X4495),X4492)
| ~ class_Rings_Oring(X4497) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).
fof(i_0_1520,plain,
! [X4486,X4487,X4488,X4489,X4490,X4491] :
( ( c_Groups_Oplus__class_Oplus(X4491,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4491),X4490),X4489),X4488) != c_Groups_Oplus__class_Oplus(X4491,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4491),X4487),X4489),X4486)
| X4488 = c_Groups_Oplus__class_Oplus(X4491,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4491),c_Groups_Ominus__class_Ominus(X4491,X4487,X4490)),X4489),X4486)
| ~ class_Rings_Oring(X4491) )
& ( X4488 != c_Groups_Oplus__class_Oplus(X4491,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4491),c_Groups_Ominus__class_Ominus(X4491,X4487,X4490)),X4489),X4486)
| c_Groups_Oplus__class_Oplus(X4491,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4491),X4490),X4489),X4488) = c_Groups_Oplus__class_Oplus(X4491,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4491),X4487),X4489),X4486)
| ~ class_Rings_Oring(X4491) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).
fof(i_0_1521,plain,
! [X4956,X4957] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4957)
| 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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X4956)),X4957),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,X4957,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X4956)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LIMSEQ__inverse__realpow__zero__lemma])]) ).
cnf(i_0_1522,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Nat_OSuc(esk75_3(X2,X1,X3))))
| hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1287]) ).
cnf(i_0_1523,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_1277]) ).
cnf(i_0_1524,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_1278]) ).
fof(i_0_1525,plain,
! [X4006] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4006) != 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,X4006,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,X4006,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,X4006,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,X4006,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])]) ).
cnf(i_0_1526,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Nat_OSuc(esk75_3(X2,X1,X3))))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1287]) ).
fof(i_0_1527,plain,
! [X4498,X4499,X4500,X4501,X4502] :
( ~ class_Rings_Oring(X4502)
| c_Groups_Ominus__class_Ominus(X4502,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4502),X4501),X4500),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4502),X4499),X4498)) = c_Groups_Oplus__class_Oplus(X4502,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4502),X4501),c_Groups_Ominus__class_Ominus(X4502,X4500,X4498)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4502),c_Groups_Ominus__class_Ominus(X4502,X4501,X4499)),X4498)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__diff__mult])]) ).
cnf(i_0_1528,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_1288]) ).
cnf(i_0_1529,plain,
( hBOOL(hAPP(X4,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X2)))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1287]) ).
fof(i_0_1530,plain,
! [X4153,X4154,X4155,X4156,X4157] :
( ~ class_Rings_Osemiring(X4157)
| c_Groups_Oplus__class_Oplus(X4157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4157),X4156),X4155),c_Groups_Oplus__class_Oplus(X4157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4157),X4154),X4155),X4153)) = c_Groups_Oplus__class_Oplus(X4157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4157),c_Groups_Oplus__class_Oplus(X4157,X4156,X4154)),X4155),X4153) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_1531,plain,
! [X5449,X5450,X5451,X5452,X5453,X5454,X5455,X5456,X5457,X5458] :
( ( X5450 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X5451,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ epred1_3(X5451,X5450,X5449) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5450)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5453)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5453,X5450)
| X5449 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5450),X5452),X5453)
| hBOOL(hAPP(X5451,X5452))
| ~ epred1_3(X5451,X5450,X5449) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5450,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5450,X5455)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5455,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5449 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5450),X5454),X5455)
| hBOOL(hAPP(X5451,X5454))
| ~ epred1_3(X5451,X5450,X5449) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5457)
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5457)
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X5456,X5457,X5458),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5457)
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk79_3(X5456,X5457,X5458)),esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5457)
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( ~ hBOOL(hAPP(X5458,esk79_3(X5456,X5457,X5458)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5457)
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,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),esk78_3(X5456,X5457,X5458))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X5456,X5457,X5458))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X5456,X5457,X5458),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),esk78_3(X5456,X5457,X5458))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk79_3(X5456,X5457,X5458)),esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X5456,X5457,X5458))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( ~ hBOOL(hAPP(X5458,esk79_3(X5456,X5457,X5458)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X5456,X5457,X5458))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X5456,X5457,X5458),X5457)
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X5456,X5457,X5458),X5457)
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X5456,X5457,X5458),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X5456,X5457,X5458),X5457)
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk79_3(X5456,X5457,X5458)),esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X5456,X5457,X5458),X5457)
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( ~ hBOOL(hAPP(X5458,esk79_3(X5456,X5457,X5458)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X5456,X5457,X5458),X5457)
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk77_3(X5456,X5457,X5458)),esk78_3(X5456,X5457,X5458))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,esk80_3(X5456,X5457,X5458))
| X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk77_3(X5456,X5457,X5458)),esk78_3(X5456,X5457,X5458))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X5456,X5457,X5458),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk77_3(X5456,X5457,X5458)),esk78_3(X5456,X5457,X5458))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk79_3(X5456,X5457,X5458)),esk80_3(X5456,X5457,X5458))
| X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk77_3(X5456,X5457,X5458)),esk78_3(X5456,X5457,X5458))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( ~ hBOOL(hAPP(X5458,esk79_3(X5456,X5457,X5458)))
| X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk77_3(X5456,X5457,X5458)),esk78_3(X5456,X5457,X5458))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5458,esk77_3(X5456,X5457,X5458)))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,esk80_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,esk77_3(X5456,X5457,X5458)))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X5456,X5457,X5458),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5458,esk77_3(X5456,X5457,X5458)))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk79_3(X5456,X5457,X5458)),esk80_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,esk77_3(X5456,X5457,X5458)))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( ~ hBOOL(hAPP(X5458,esk79_3(X5456,X5457,X5458)))
| ~ hBOOL(hAPP(X5458,esk77_3(X5456,X5457,X5458)))
| X5457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5457)
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5457)
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X5456,X5457,X5458),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5457)
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk79_3(X5456,X5457,X5458)),esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5457)
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( ~ hBOOL(hAPP(X5458,esk79_3(X5456,X5457,X5458)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5457)
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,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),esk78_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X5456,X5457,X5458),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),esk78_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk79_3(X5456,X5457,X5458)),esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( ~ hBOOL(hAPP(X5458,esk79_3(X5456,X5457,X5458)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X5456,X5457,X5458),X5457)
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X5456,X5457,X5458),X5457)
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X5456,X5457,X5458),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X5456,X5457,X5458),X5457)
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk79_3(X5456,X5457,X5458)),esk80_3(X5456,X5457,X5458))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X5456,X5457,X5458),X5457)
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( ~ hBOOL(hAPP(X5458,esk79_3(X5456,X5457,X5458)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X5456,X5457,X5458),X5457)
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk77_3(X5456,X5457,X5458)),esk78_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,esk80_3(X5456,X5457,X5458))
| X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk77_3(X5456,X5457,X5458)),esk78_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X5456,X5457,X5458),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk77_3(X5456,X5457,X5458)),esk78_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk79_3(X5456,X5457,X5458)),esk80_3(X5456,X5457,X5458))
| X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk77_3(X5456,X5457,X5458)),esk78_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( ~ hBOOL(hAPP(X5458,esk79_3(X5456,X5457,X5458)))
| X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk77_3(X5456,X5457,X5458)),esk78_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5458,esk77_3(X5456,X5457,X5458)))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5457,esk80_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,esk77_3(X5456,X5457,X5458)))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X5456,X5457,X5458),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5458,esk77_3(X5456,X5457,X5458)))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( X5456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5457),esk79_3(X5456,X5457,X5458)),esk80_3(X5456,X5457,X5458))
| ~ hBOOL(hAPP(X5458,esk77_3(X5456,X5457,X5458)))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) )
& ( ~ hBOOL(hAPP(X5458,esk79_3(X5456,X5457,X5458)))
| ~ hBOOL(hAPP(X5458,esk77_3(X5456,X5457,X5458)))
| ~ hBOOL(hAPP(X5458,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X5458,X5457,X5456) ) ),
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_1261])])])])])]) ).
fof(i_0_1532,plain,
! [X4669,X4670,X4671,X4672,X4673,X4674] :
( ~ class_Rings_Olinordered__semiring__1__strict(X4674)
| ~ c_Orderings_Oord__class_Oless(X4674,X4673,X4672)
| ~ c_Orderings_Oord__class_Oless(X4674,X4671,X4672)
| ~ c_Orderings_Oord__class_Oless__eq(X4674,c_Groups_Ozero__class_Ozero(X4674),X4670)
| ~ c_Orderings_Oord__class_Oless__eq(X4674,c_Groups_Ozero__class_Ozero(X4674),X4669)
| c_Groups_Oplus__class_Oplus(X4674,X4670,X4669) != c_Groups_Oone__class_Oone(X4674)
| c_Orderings_Oord__class_Oless(X4674,c_Groups_Oplus__class_Oplus(X4674,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4674),X4670),X4673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4674),X4669),X4671)),X4672) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).
fof(i_0_1533,plain,
! [X4660,X4661,X4662,X4663,X4664,X4665] :
( ~ class_Rings_Olinordered__semiring__1(X4665)
| ~ c_Orderings_Oord__class_Oless__eq(X4665,X4664,X4663)
| ~ c_Orderings_Oord__class_Oless__eq(X4665,X4662,X4663)
| ~ c_Orderings_Oord__class_Oless__eq(X4665,c_Groups_Ozero__class_Ozero(X4665),X4661)
| ~ c_Orderings_Oord__class_Oless__eq(X4665,c_Groups_Ozero__class_Ozero(X4665),X4660)
| c_Groups_Oplus__class_Oplus(X4665,X4661,X4660) != c_Groups_Oone__class_Oone(X4665)
| c_Orderings_Oord__class_Oless__eq(X4665,c_Groups_Oplus__class_Oplus(X4665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4665),X4661),X4664),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4665),X4660),X4662)),X4663) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).
fof(i_0_1534,plain,
! [X4039,X4040,X4041] :
( ~ class_RealVector_Oreal__normed__vector(X4041)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4040)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4041,hAPP(X4039,esk54_3(X4039,X4040,X4041))),X4040)
| c_SEQ_OBseq(X4041,X4039) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_BseqI])])]) ).
fof(i_0_1535,plain,
! [X4025,X4026,X4028,X4029] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk51_2(X4025,X4026))
| ~ c_SEQ_OBseq(X4026,X4025)
| ~ class_RealVector_Oreal__normed__vector(X4026) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4026,hAPP(X4025,X4028)),esk51_2(X4025,X4026))
| ~ c_SEQ_OBseq(X4026,X4025)
| ~ class_RealVector_Oreal__normed__vector(X4026) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4026,hAPP(X4025,esk52_3(X4025,X4026,X4029))),X4029)
| c_SEQ_OBseq(X4026,X4025)
| ~ class_RealVector_Oreal__normed__vector(X4026) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Bseq__def])])])])]) ).
fof(i_0_1536,plain,
! [X4876,X4877,X4878,X4879] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4879),X4878),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4877),X4878),X4876)) = 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,X4879,X4877)),X4878),X4876),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
cnf(i_0_1537,plain,
( X2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(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_1289]) ).
fof(i_0_1538,plain,
! [X4605,X4606,X4607] :
( ( ~ c_Orderings_Oord__class_Oless(X4607,c_Groups_Ozero__class_Ozero(X4607),c_Groups_Oplus__class_Oplus(X4607,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4607),X4606),X4606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4607),X4605),X4605)))
| X4606 != c_Groups_Ozero__class_Ozero(X4607)
| X4605 != c_Groups_Ozero__class_Ozero(X4607)
| ~ class_Rings_Olinordered__ring__strict(X4607) )
& ( X4606 = c_Groups_Ozero__class_Ozero(X4607)
| c_Orderings_Oord__class_Oless(X4607,c_Groups_Ozero__class_Ozero(X4607),c_Groups_Oplus__class_Oplus(X4607,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4607),X4606),X4606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4607),X4605),X4605)))
| ~ class_Rings_Olinordered__ring__strict(X4607) )
& ( X4605 = c_Groups_Ozero__class_Ozero(X4607)
| c_Orderings_Oord__class_Oless(X4607,c_Groups_Ozero__class_Ozero(X4607),c_Groups_Oplus__class_Oplus(X4607,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4607),X4606),X4606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4607),X4605),X4605)))
| ~ class_Rings_Olinordered__ring__strict(X4607) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).
fof(i_0_1539,plain,
! [X4204,X4205,X4206,X4207,X4208] :
( ~ class_Rings_Ocomm__semiring__1(X4208)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4208),X4207),X4206)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4208),X4205),X4204)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4208),X4205),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4208),X4207),X4206)),X4204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).
fof(i_0_1540,plain,
! [X4596,X4597,X4598] :
( ( X4597 = c_Groups_Ozero__class_Ozero(X4598)
| ~ c_Orderings_Oord__class_Oless__eq(X4598,c_Groups_Oplus__class_Oplus(X4598,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),X4597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4596),X4596)),c_Groups_Ozero__class_Ozero(X4598))
| ~ class_Rings_Olinordered__ring__strict(X4598) )
& ( X4596 = c_Groups_Ozero__class_Ozero(X4598)
| ~ c_Orderings_Oord__class_Oless__eq(X4598,c_Groups_Oplus__class_Oplus(X4598,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),X4597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4596),X4596)),c_Groups_Ozero__class_Ozero(X4598))
| ~ class_Rings_Olinordered__ring__strict(X4598) )
& ( X4597 != c_Groups_Ozero__class_Ozero(X4598)
| X4596 != c_Groups_Ozero__class_Ozero(X4598)
| c_Orderings_Oord__class_Oless__eq(X4598,c_Groups_Oplus__class_Oplus(X4598,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4597),X4597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4598),X4596),X4596)),c_Groups_Ozero__class_Ozero(X4598))
| ~ class_Rings_Olinordered__ring__strict(X4598) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).
fof(i_0_1541,plain,
! [X4602,X4603,X4604] :
( ~ class_Rings_Olinordered__ring(X4604)
| ~ c_Orderings_Oord__class_Oless(X4604,c_Groups_Oplus__class_Oplus(X4604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4604),X4603),X4603),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4604),X4602),X4602)),c_Groups_Ozero__class_Ozero(X4604)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1290])]) ).
cnf(i_0_1542,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_1291]) ).
fof(i_0_1543,plain,
! [X5004,X5005,X5006] :
( ~ class_Groups_Omonoid__mult(X5006)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5005)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5006),hAPP(hAPP(c_Power_Opower__class_Opower(X5006),X5004),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5005,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X5004) = hAPP(hAPP(c_Power_Opower__class_Opower(X5006),X5004),X5005) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__minus__mult])]) ).
cnf(i_0_1544,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_1292]) ).
fof(i_0_1545,plain,
! [X3812,X3813,X3814,X3816] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_3(X3812,X3813,X3814))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3813,X3812)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3814,X3813) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3814,X3816)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3813,X3816)),esk33_3(X3812,X3813,X3814))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3813,X3812)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3814,X3813) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3816,X3812)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3813,X3816)),esk33_3(X3812,X3813,X3814))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3813,X3812)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3814,X3813) ) ),
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__interval])])])])]) ).
fof(i_0_1546,plain,
! [X4175,X4176,X4177,X4178,X4179] :
( ( X4178 = X4177
| X4176 = X4175
| c_Groups_Oplus__class_Oplus(X4179,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4178),X4176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4177),X4175)) != c_Groups_Oplus__class_Oplus(X4179,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4178),X4175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4177),X4176))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4179) )
& ( X4178 != X4177
| c_Groups_Oplus__class_Oplus(X4179,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4178),X4176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4177),X4175)) = c_Groups_Oplus__class_Oplus(X4179,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4178),X4175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4177),X4176))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4179) )
& ( X4176 != X4175
| c_Groups_Oplus__class_Oplus(X4179,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4178),X4176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4177),X4175)) = c_Groups_Oplus__class_Oplus(X4179,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4178),X4175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4179),X4177),X4176))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4179) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_1547,plain,
! [X4162,X4163,X4164,X4165,X4166] :
( ( c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4165),X4164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4163),X4162)) != c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4165),X4162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4163),X4164))
| X4165 = X4163
| X4164 = X4162
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4166) )
& ( X4165 != X4163
| c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4165),X4164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4163),X4162)) = c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4165),X4162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4163),X4164))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4166) )
& ( X4164 != X4162
| c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4165),X4164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4163),X4162)) = c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4165),X4162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4163),X4164))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4166) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
fof(i_0_1548,plain,
! [X3778,X3779,X3780,X3781] :
( ( c_Orderings_Oord__class_Oless(X3781,c_Groups_Ominus__class_Ominus(X3781,X3779,X3778),X3780)
| ~ c_Orderings_Oord__class_Oless(X3781,c_Groups_Oabs__class_Oabs(X3781,c_Groups_Ominus__class_Ominus(X3781,X3780,X3779)),X3778)
| ~ class_Rings_Olinordered__idom(X3781) )
& ( c_Orderings_Oord__class_Oless(X3781,X3780,c_Groups_Oplus__class_Oplus(X3781,X3779,X3778))
| ~ c_Orderings_Oord__class_Oless(X3781,c_Groups_Oabs__class_Oabs(X3781,c_Groups_Ominus__class_Ominus(X3781,X3780,X3779)),X3778)
| ~ class_Rings_Olinordered__idom(X3781) )
& ( ~ c_Orderings_Oord__class_Oless(X3781,c_Groups_Ominus__class_Ominus(X3781,X3779,X3778),X3780)
| ~ c_Orderings_Oord__class_Oless(X3781,X3780,c_Groups_Oplus__class_Oplus(X3781,X3779,X3778))
| c_Orderings_Oord__class_Oless(X3781,c_Groups_Oabs__class_Oabs(X3781,c_Groups_Ominus__class_Ominus(X3781,X3780,X3779)),X3778)
| ~ class_Rings_Olinordered__idom(X3781) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff])])]) ).
cnf(i_0_1549,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_1293]) ).
cnf(i_0_1550,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_1294]) ).
fof(i_0_1551,plain,
! [X4115,X4116,X4117,X4118] :
( ~ class_Int_Onumber__ring(X4118)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4118),c_Int_Onumber__class_Onumber__of(X4118,X4117)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4118),c_Int_Onumber__class_Onumber__of(X4118,X4116)),X4115)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4118),c_Int_Onumber__class_Onumber__of(X4118,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4117),X4116))),X4115) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).
cnf(i_0_1552,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(esk21_2(X2,X1))),hAPP(X2,esk21_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1295]) ).
cnf(i_0_1553,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(esk15_2(X2,X1))),hAPP(X2,esk15_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1296]) ).
cnf(i_0_1554,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk22_2(X2,X1)),hAPP(X2,c_Nat_OSuc(esk22_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1297]) ).
cnf(i_0_1555,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk14_2(X2,X1)),hAPP(X2,c_Nat_OSuc(esk14_2(X2,X1))))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1296]) ).
cnf(i_0_1556,plain,
( c_SEQ_Oincseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk16_2(X2,X1)),hAPP(X2,c_Nat_OSuc(esk16_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1298]) ).
fof(i_0_1557,plain,
! [X4838,X4839,X4840] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4840,c_Int_OPls)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4840)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4839)),X4838)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4840,c_Int_OPls)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4840)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4839)),X4838)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4840),X4839))),X4838) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1299])]) ).
fof(i_0_1558,plain,
! [X4844,X4845,X4846] :
( ~ 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),X4846),X4845),X4844),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),X4844)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4846)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4845,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_1559,plain,
! [X4841,X4842,X4843] :
( ~ 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),X4843),X4842),X4841))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4841,X4843)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4843)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4842) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).
fof(i_0_1560,plain,
! [X5344,X5345,X5346,X5347,X5348,X5349,X5350,X5351] :
( ( X5344 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X5346,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5345,X5344))) )
& ( X5344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5348,X5344)
| X5345 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5344),X5347),X5348)
| hBOOL(hAPP(X5346,X5347))
| ~ hBOOL(hAPP(X5346,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5345,X5344))) )
& ( X5349 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X5349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5351,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5350,X5349))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk74_3(X5349,X5350,X5351),X5349)
| X5349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5351,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5350,X5349))) )
& ( X5350 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5349),esk73_3(X5349,X5350,X5351)),esk74_3(X5349,X5350,X5351))
| X5349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5351,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5350,X5349))) )
& ( ~ hBOOL(hAPP(X5351,esk73_3(X5349,X5350,X5351)))
| X5349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5351,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5350,X5349))) )
& ( X5349 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X5351,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X5351,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5350,X5349))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk74_3(X5349,X5350,X5351),X5349)
| ~ hBOOL(hAPP(X5351,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X5351,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5350,X5349))) )
& ( X5350 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5349),esk73_3(X5349,X5350,X5351)),esk74_3(X5349,X5350,X5351))
| ~ hBOOL(hAPP(X5351,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X5351,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5350,X5349))) )
& ( ~ hBOOL(hAPP(X5351,esk73_3(X5349,X5350,X5351)))
| ~ hBOOL(hAPP(X5351,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X5351,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5350,X5349))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div])])])])])]) ).
fof(i_0_1561,plain,
! [X3769,X3770,X3771] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3771)
| c_Orderings_Oord__class_Oless__eq(X3771,c_Groups_Oabs__class_Oabs(X3771,c_Groups_Ominus__class_Ominus(X3771,c_Groups_Oabs__class_Oabs(X3771,X3770),c_Groups_Oabs__class_Oabs(X3771,X3769))),c_Groups_Oabs__class_Oabs(X3771,c_Groups_Ominus__class_Ominus(X3771,X3770,X3769))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).
fof(i_0_1562,plain,
! [X3922,X3923,X3924] :
( ~ class_RealVector_Oreal__normed__vector(X3924)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3924,X3923),c_RealVector_Onorm__class_Onorm(X3924,X3922))),c_RealVector_Onorm__class_Onorm(X3924,c_Groups_Ominus__class_Ominus(X3924,X3923,X3922))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq3])]) ).
fof(i_0_1563,plain,
! [X4199,X4200,X4201,X4202,X4203] :
( ~ class_Rings_Ocomm__semiring__1(X4203)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4203),X4202),X4201)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4203),X4200),X4199)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4203),X4202),X4200)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4203),X4201),X4199)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).
fof(i_0_1564,plain,
! [X4209,X4210,X4211,X4212,X4213] :
( ~ class_Rings_Ocomm__semiring__1(X4213)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4213),X4212),X4211)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4213),X4210),X4209)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4213),X4212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4213),X4211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4213),X4210),X4209))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).
cnf(i_0_1565,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_1300]) ).
cnf(i_0_1566,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_1301]) ).
cnf(i_0_1567,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_1302]) ).
cnf(i_0_1568,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_1303]) ).
fof(i_0_1569,plain,
! [X4516,X4517,X4518,X4519] :
( ~ class_Int_Onumber(X4519)
| ~ class_Rings_Oring(X4519)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4519),c_Int_Onumber__class_Onumber__of(X4519,X4518)),c_Groups_Ominus__class_Ominus(X4519,X4517,X4516)) = c_Groups_Ominus__class_Ominus(X4519,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4519),c_Int_Onumber__class_Onumber__of(X4519,X4518)),X4517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4519),c_Int_Onumber__class_Onumber__of(X4519,X4518)),X4516)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])]) ).
fof(i_0_1570,plain,
! [X4469,X4470,X4471,X4472] :
( ~ class_Int_Onumber(X4472)
| ~ class_Rings_Osemiring(X4472)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4472),c_Int_Onumber__class_Onumber__of(X4472,X4471)),c_Groups_Oplus__class_Oplus(X4472,X4470,X4469)) = c_Groups_Oplus__class_Oplus(X4472,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4472),c_Int_Onumber__class_Onumber__of(X4472,X4471)),X4470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4472),c_Int_Onumber__class_Onumber__of(X4472,X4471)),X4469)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).
fof(i_0_1571,plain,
! [X3969,X3970] : 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,X3970,X3969)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3970)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3969)),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__ineq2]) ).
fof(i_0_1572,plain,
! [X3877,X3878] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3878),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3878,X3877)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3877))),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__sub]) ).
cnf(i_0_1573,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_1304]) ).
cnf(i_0_1574,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X2,c_Nat_OSuc(X3)))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Nat_OSuc(X4)),hAPP(X2,X4))
| ~ c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1296]) ).
fof(i_0_1575,plain,
! [X3265,X3266,X3267,X3268,X3269,X3270,X3271] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3266,X3265)
| hBOOL(hAPP(X3267,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X3267,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3266,X3265))) )
& ( X3266 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3265,X3268)
| hBOOL(hAPP(X3267,X3268))
| ~ hBOOL(hAPP(X3267,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3266,X3265))) )
& ( X3270 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3269,esk26_3(X3269,X3270,X3271))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3270,X3269)
| hBOOL(hAPP(X3271,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3270,X3269))) )
& ( ~ hBOOL(hAPP(X3271,esk26_3(X3269,X3270,X3271)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3270,X3269)
| hBOOL(hAPP(X3271,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3270,X3269))) )
& ( X3270 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3269,esk26_3(X3269,X3270,X3271))
| ~ hBOOL(hAPP(X3271,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X3271,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3270,X3269))) )
& ( ~ hBOOL(hAPP(X3271,esk26_3(X3269,X3270,X3271)))
| ~ hBOOL(hAPP(X3271,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X3271,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3270,X3269))) ) ),
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_1305])])])])])]) ).
fof(i_0_1576,plain,
! [X3257,X3258,X3259,X3260,X3261,X3262,X3263] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3258,X3257)
| hBOOL(hAPP(X3259,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X3259,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3258,X3257))) )
& ( X3258 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3257,X3260)
| hBOOL(hAPP(X3259,X3260))
| ~ hBOOL(hAPP(X3259,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3258,X3257))) )
& ( X3262 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3261,esk25_3(X3261,X3262,X3263))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3262,X3261)
| hBOOL(hAPP(X3263,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3262,X3261))) )
& ( ~ hBOOL(hAPP(X3263,esk25_3(X3261,X3262,X3263)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3262,X3261)
| hBOOL(hAPP(X3263,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3262,X3261))) )
& ( X3262 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3261,esk25_3(X3261,X3262,X3263))
| ~ hBOOL(hAPP(X3263,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X3263,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3262,X3261))) )
& ( ~ hBOOL(hAPP(X3263,esk25_3(X3261,X3262,X3263)))
| ~ hBOOL(hAPP(X3263,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X3263,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3262,X3261))) ) ),
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_1577,plain,
! [X4524,X4525,X4526,X4527,X4528] :
( ~ class_Rings_Olinordered__idom(X4528)
| ~ c_Orderings_Oord__class_Oless(X4528,c_Groups_Oabs__class_Oabs(X4528,X4527),X4526)
| ~ c_Orderings_Oord__class_Oless(X4528,c_Groups_Oabs__class_Oabs(X4528,X4525),X4524)
| c_Orderings_Oord__class_Oless(X4528,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4528),c_Groups_Oabs__class_Oabs(X4528,X4527)),c_Groups_Oabs__class_Oabs(X4528,X4525)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4528),X4526),X4524)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).
cnf(i_0_1578,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_1306]) ).
cnf(i_0_1579,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_1307]) ).
fof(i_0_1580,plain,
! [X4520,X4521,X4522,X4523] :
( ~ class_Int_Onumber(X4523)
| ~ class_Rings_Oring(X4523)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4523),c_Groups_Ominus__class_Ominus(X4523,X4522,X4521)),c_Int_Onumber__class_Onumber__of(X4523,X4520)) = c_Groups_Ominus__class_Ominus(X4523,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4523),X4522),c_Int_Onumber__class_Onumber__of(X4523,X4520)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4523),X4521),c_Int_Onumber__class_Onumber__of(X4523,X4520))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of])]) ).
fof(i_0_1581,plain,
! [X4465,X4466,X4467,X4468] :
( ~ class_Int_Onumber(X4468)
| ~ class_Rings_Osemiring(X4468)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4468),c_Groups_Oplus__class_Oplus(X4468,X4467,X4466)),c_Int_Onumber__class_Onumber__of(X4468,X4465)) = c_Groups_Oplus__class_Oplus(X4468,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4468),X4467),c_Int_Onumber__class_Onumber__of(X4468,X4465)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4468),X4466),c_Int_Onumber__class_Onumber__of(X4468,X4465))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).
fof(i_0_1582,plain,
! [X3973,X3975] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3973)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk43_1(X3973),X3975)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X3975)),v_z____)),X3973) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fz_I2_J])])])]) ).
fof(i_0_1583,plain,
! [X5156,X5157,X5158] :
( ~ class_Rings_Olinordered__semidom(X5158)
| ~ c_Orderings_Oord__class_Oless(X5158,c_Groups_Ozero__class_Ozero(X5158),X5157)
| ~ c_Orderings_Oord__class_Oless(X5158,X5157,c_Groups_Oone__class_Oone(X5158))
| c_Orderings_Oord__class_Oless(X5158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5158),X5157),hAPP(hAPP(c_Power_Opower__class_Opower(X5158),X5157),X5156)),hAPP(hAPP(c_Power_Opower__class_Opower(X5158),X5157),X5156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
fof(i_0_1584,plain,
! [X4087,X4088,X4089] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4089,X4088)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4087)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4087)),X4089),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4087)),X4088)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma])]) ).
fof(i_0_1585,plain,
! [X3830] :
( ( ~ 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),X3830),X3830),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3830,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3830,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),X3830),X3830),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_1586,plain,
! [X3964,X3965,X3966,X3967,X3968] :
( ~ class_RealVector_Oreal__normed__vector(X3968)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3968,X3967),X3966)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3968,X3965),X3964)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3968,c_Groups_Oplus__class_Oplus(X3968,X3967,X3965)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3966,X3964)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__add__less])]) ).
cnf(i_0_1587,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_1308]) ).
cnf(i_0_1588,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,c_Nat_OSuc(X3),X4) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,X3,hAPP(X2,X4))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1309]) ).
fof(i_0_1589,plain,
! [X4834,X4835] :
( ( X4835 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4835),X4834) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4835 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4835),X4834) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4834,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4835,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4834)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).
fof(i_0_1590,plain,
! [X3234,X3235,X3236] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3235,X3236),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3234,X3236))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3235,X3234)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3236,X3234)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3236,X3235) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3235,X3234)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3235,X3236),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3234,X3236))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3236,X3234)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3236,X3235) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).
fof(i_0_1591,plain,
! [X3424,X3425,X3426] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3425,X3426),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3424,X3426))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3425,X3424)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3426,X3424)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3426,X3425) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3425,X3424)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3425,X3426),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3424,X3426))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3426,X3424)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3426,X3425) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).
fof(i_0_1592,plain,
! [X4551,X4552,X4553,X4554,X4555] :
( ~ class_Rings_Olinordered__semiring__strict(X4555)
| ~ c_Orderings_Oord__class_Oless(X4555,X4554,X4553)
| ~ c_Orderings_Oord__class_Oless(X4555,X4552,X4551)
| ~ c_Orderings_Oord__class_Oless(X4555,c_Groups_Ozero__class_Ozero(X4555),X4553)
| ~ c_Orderings_Oord__class_Oless__eq(X4555,c_Groups_Ozero__class_Ozero(X4555),X4552)
| c_Orderings_Oord__class_Oless(X4555,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4555),X4554),X4552),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4555),X4553),X4551)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).
fof(i_0_1593,plain,
! [X4556,X4557,X4558,X4559,X4560] :
( ~ class_Rings_Olinordered__semiring__strict(X4560)
| ~ c_Orderings_Oord__class_Oless(X4560,X4559,X4558)
| ~ c_Orderings_Oord__class_Oless(X4560,X4557,X4556)
| ~ c_Orderings_Oord__class_Oless__eq(X4560,c_Groups_Ozero__class_Ozero(X4560),X4559)
| ~ c_Orderings_Oord__class_Oless__eq(X4560,c_Groups_Ozero__class_Ozero(X4560),X4557)
| c_Orderings_Oord__class_Oless(X4560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4560),X4559),X4557),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4560),X4558),X4556)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).
fof(i_0_1594,plain,
! [X4566,X4567,X4568,X4569,X4570] :
( ~ class_Rings_Olinordered__semiring__strict(X4570)
| ~ c_Orderings_Oord__class_Oless__eq(X4570,X4569,X4568)
| ~ c_Orderings_Oord__class_Oless(X4570,X4567,X4566)
| ~ c_Orderings_Oord__class_Oless(X4570,c_Groups_Ozero__class_Ozero(X4570),X4569)
| ~ c_Orderings_Oord__class_Oless__eq(X4570,c_Groups_Ozero__class_Ozero(X4570),X4567)
| c_Orderings_Oord__class_Oless(X4570,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4570),X4569),X4567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4570),X4568),X4566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).
fof(i_0_1595,plain,
! [X4561,X4562,X4563,X4564,X4565] :
( ~ class_Rings_Olinordered__semiring__strict(X4565)
| ~ c_Orderings_Oord__class_Oless(X4565,X4564,X4563)
| ~ c_Orderings_Oord__class_Oless__eq(X4565,X4562,X4561)
| ~ c_Orderings_Oord__class_Oless__eq(X4565,c_Groups_Ozero__class_Ozero(X4565),X4564)
| ~ c_Orderings_Oord__class_Oless(X4565,c_Groups_Ozero__class_Ozero(X4565),X4562)
| c_Orderings_Oord__class_Oless(X4565,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4565),X4564),X4562),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4565),X4563),X4561)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).
fof(i_0_1596,plain,
! [X4355,X4356,X4357,X4358,X4359] :
( ~ class_Rings_Oordered__semiring(X4359)
| ~ c_Orderings_Oord__class_Oless__eq(X4359,X4358,X4357)
| ~ c_Orderings_Oord__class_Oless__eq(X4359,X4356,X4355)
| ~ c_Orderings_Oord__class_Oless__eq(X4359,c_Groups_Ozero__class_Ozero(X4359),X4358)
| ~ c_Orderings_Oord__class_Oless__eq(X4359,c_Groups_Ozero__class_Ozero(X4359),X4356)
| c_Orderings_Oord__class_Oless__eq(X4359,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4359),X4358),X4356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4359),X4357),X4355)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).
fof(i_0_1597,plain,
! [X4360,X4361,X4362,X4363,X4364] :
( ~ class_Rings_Oordered__semiring(X4364)
| ~ c_Orderings_Oord__class_Oless__eq(X4364,X4363,X4362)
| ~ c_Orderings_Oord__class_Oless__eq(X4364,X4361,X4360)
| ~ c_Orderings_Oord__class_Oless__eq(X4364,c_Groups_Ozero__class_Ozero(X4364),X4362)
| ~ c_Orderings_Oord__class_Oless__eq(X4364,c_Groups_Ozero__class_Ozero(X4364),X4361)
| c_Orderings_Oord__class_Oless__eq(X4364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4364),X4363),X4361),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4364),X4362),X4360)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).
fof(i_0_1598,plain,
! [X4268,X4269,X4270,X4271,X4272] :
( ~ class_RealVector_Oreal__normed__algebra(X4272)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4272,X4271),X4270)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4272,X4269),X4268)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4272,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4272),X4271),X4269)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4270),X4268)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__less])]) ).
fof(i_0_1599,plain,
! [X5292,X5293,X5294,X5295] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5294)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5294)
| X5294 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5295,X5294) = X5293
| X5295 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5294),X5293),X5292) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5294,X5292)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5292,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5294)
| X5294 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5295,X5294) = X5293
| X5295 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5294),X5293),X5292) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5294)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5292)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5292,X5294)
| X5294 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5295,X5294) = X5293
| X5295 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5294),X5293),X5292) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5294,X5292)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5292,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),X5292)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5292,X5294)
| X5294 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5295,X5294) = X5293
| X5295 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5294),X5293),X5292) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1310])])]) ).
fof(i_0_1600,plain,
! [X5062,X5063,X5064,X5065] :
( ~ class_Groups_Ocomm__monoid__mult(X5065)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5065),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5065),X5064),X5063)),X5062) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5065),hAPP(hAPP(c_Power_Opower__class_Opower(X5065),X5064),X5062)),hAPP(hAPP(c_Power_Opower__class_Opower(X5065),X5063),X5062)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_1601,plain,
! [X4987,X4988,X4989,X4990] :
( ~ class_Rings_Ocomm__semiring__1(X4990)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4990),X4989),X4988)),X4987) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4990),hAPP(hAPP(c_Power_Opower__class_Opower(X4990),X4989),X4987)),hAPP(hAPP(c_Power_Opower__class_Opower(X4990),X4988),X4987)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_1602,plain,
! [X3688,X3689,X3690] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3690,X3689)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3689,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3690,X3688))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3689,X3690)),X3688) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ath])]) ).
cnf(i_0_1603,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1))
| ~ 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,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1311]) ).
fof(i_0_1604,plain,
! [X4599,X4600,X4601] :
( ~ class_Rings_Olinordered__ring(X4601)
| c_Orderings_Oord__class_Oless__eq(X4601,c_Groups_Ozero__class_Ozero(X4601),c_Groups_Oplus__class_Oplus(X4601,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4601),X4600),X4600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4601),X4599),X4599))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).
cnf(i_0_1605,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_1312]) ).
fof(i_0_1606,plain,
! [X4645,X4646] :
( ~ class_Rings_Oring__1(X4646)
| c_Groups_Ominus__class_Ominus(X4646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4646),X4645),X4645),c_Groups_Oone__class_Oone(X4646)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4646),c_Groups_Oplus__class_Oplus(X4646,X4645,c_Groups_Oone__class_Oone(X4646))),c_Groups_Ominus__class_Ominus(X4646,X4645,c_Groups_Oone__class_Oone(X4646))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored])]) ).
cnf(i_0_1607,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_1294]) ).
cnf(i_0_1608,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_1294]) ).
cnf(i_0_1609,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_1313]) ).
cnf(i_0_1610,plain,
( c_SEQ_Osubseq(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,esk30_1(X1)),hAPP(X1,c_Nat_OSuc(esk30_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1314]) ).
fof(i_0_1611,plain,
! [X5126,X5127,X5128] :
( ~ class_Rings_Olinordered__semidom(X5128)
| ~ c_Orderings_Oord__class_Oless(X5128,c_Groups_Oone__class_Oone(X5128),X5127)
| c_Orderings_Oord__class_Oless(X5128,hAPP(hAPP(c_Power_Opower__class_Opower(X5128),X5127),X5126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5128),X5127),hAPP(hAPP(c_Power_Opower__class_Opower(X5128),X5127),X5126))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
fof(i_0_1612,plain,
! [X4571,X4572,X4573,X4574] :
( ~ class_Rings_Olinordered__semiring(X4574)
| ~ c_Orderings_Oord__class_Oless(X4574,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4574),X4573),X4572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4574),X4571),X4572))
| ~ c_Orderings_Oord__class_Oless__eq(X4574,c_Groups_Ozero__class_Ozero(X4574),X4572)
| c_Orderings_Oord__class_Oless(X4574,X4573,X4571) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).
fof(i_0_1613,plain,
! [X4575,X4576,X4577,X4578] :
( ~ class_Rings_Olinordered__semiring__strict(X4578)
| ~ c_Orderings_Oord__class_Oless(X4578,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4578),X4577),X4576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4578),X4575),X4576))
| ~ c_Orderings_Oord__class_Oless__eq(X4578,c_Groups_Ozero__class_Ozero(X4578),X4576)
| c_Orderings_Oord__class_Oless(X4578,X4577,X4575) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).
fof(i_0_1614,plain,
! [X5114,X5115,X5116,X5117] :
( ~ class_Rings_Olinordered__semidom(X5117)
| ~ c_Orderings_Oord__class_Oless(X5117,hAPP(hAPP(c_Power_Opower__class_Opower(X5117),X5116),X5115),hAPP(hAPP(c_Power_Opower__class_Opower(X5117),X5114),X5115))
| ~ c_Orderings_Oord__class_Oless__eq(X5117,c_Groups_Ozero__class_Ozero(X5117),X5114)
| c_Orderings_Oord__class_Oless(X5117,X5116,X5114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).
fof(i_0_1615,plain,
! [X4579,X4580,X4581,X4582] :
( ~ class_Rings_Olinordered__semiring(X4582)
| ~ c_Orderings_Oord__class_Oless(X4582,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4582),X4581),X4580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4582),X4581),X4579))
| ~ c_Orderings_Oord__class_Oless__eq(X4582,c_Groups_Ozero__class_Ozero(X4582),X4581)
| c_Orderings_Oord__class_Oless(X4582,X4580,X4579) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).
fof(i_0_1616,plain,
! [X4583,X4584,X4585,X4586] :
( ~ class_Rings_Olinordered__semiring__strict(X4586)
| ~ c_Orderings_Oord__class_Oless(X4586,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4586),X4585),X4584),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4586),X4585),X4583))
| ~ c_Orderings_Oord__class_Oless__eq(X4586,c_Groups_Ozero__class_Ozero(X4586),X4585)
| c_Orderings_Oord__class_Oless(X4586,X4584,X4583) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).
fof(i_0_1617,plain,
! [X4381,X4382,X4383,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),X4383),X4381))
| c_Orderings_Oord__class_Oless(X4384,X4382,X4381)
| ~ c_Orderings_Oord__class_Oless(X4384,c_Groups_Ozero__class_Ozero(X4384),X4383)
| ~ class_Rings_Olinordered__ring__strict(X4384) )
& ( ~ c_Orderings_Oord__class_Oless(X4384,X4382,X4381)
| c_Orderings_Oord__class_Oless(X4384,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4384),X4383),X4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4384),X4383),X4381))
| ~ c_Orderings_Oord__class_Oless(X4384,c_Groups_Ozero__class_Ozero(X4384),X4383)
| ~ class_Rings_Olinordered__ring__strict(X4384) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).
fof(i_0_1618,plain,
! [X4587,X4588,X4589,X4590] :
( ~ class_Rings_Olinordered__semiring__strict(X4590)
| ~ c_Orderings_Oord__class_Oless__eq(X4590,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4590),X4589),X4588),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4590),X4587),X4588))
| ~ c_Orderings_Oord__class_Oless(X4590,c_Groups_Ozero__class_Ozero(X4590),X4588)
| c_Orderings_Oord__class_Oless__eq(X4590,X4589,X4587) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).
fof(i_0_1619,plain,
! [X4591,X4592,X4593,X4594] :
( ~ class_Rings_Olinordered__semiring__strict(X4594)
| ~ c_Orderings_Oord__class_Oless__eq(X4594,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4594),X4593),X4592),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4594),X4593),X4591))
| ~ c_Orderings_Oord__class_Oless(X4594,c_Groups_Ozero__class_Ozero(X4594),X4593)
| c_Orderings_Oord__class_Oless__eq(X4594,X4592,X4591) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).
fof(i_0_1620,plain,
! [X4543,X4544,X4545,X4546] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4546,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4546),X4545),X4544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4546),X4545),X4543))
| c_Orderings_Oord__class_Oless__eq(X4546,X4544,X4543)
| ~ c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),X4545)
| ~ class_Rings_Olinordered__ring__strict(X4546) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4546,X4544,X4543)
| c_Orderings_Oord__class_Oless__eq(X4546,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4546),X4545),X4544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4546),X4545),X4543))
| ~ c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),X4545)
| ~ class_Rings_Olinordered__ring__strict(X4546) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).
fof(i_0_1621,plain,
! [X4400,X4401,X4402,X4403] :
( ( ~ c_Orderings_Oord__class_Oless(X4403,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4403),X4402),X4401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4403),X4402),X4400))
| c_Orderings_Oord__class_Oless(X4403,X4400,X4401)
| ~ c_Orderings_Oord__class_Oless(X4403,X4402,c_Groups_Ozero__class_Ozero(X4403))
| ~ class_Rings_Olinordered__ring__strict(X4403) )
& ( ~ c_Orderings_Oord__class_Oless(X4403,X4400,X4401)
| c_Orderings_Oord__class_Oless(X4403,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4403),X4402),X4401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4403),X4402),X4400))
| ~ c_Orderings_Oord__class_Oless(X4403,X4402,c_Groups_Ozero__class_Ozero(X4403))
| ~ class_Rings_Olinordered__ring__strict(X4403) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).
fof(i_0_1622,plain,
! [X4547,X4548,X4549,X4550] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4550,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4550),X4549),X4548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4550),X4549),X4547))
| c_Orderings_Oord__class_Oless__eq(X4550,X4547,X4548)
| ~ c_Orderings_Oord__class_Oless(X4550,X4549,c_Groups_Ozero__class_Ozero(X4550))
| ~ class_Rings_Olinordered__ring__strict(X4550) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4550,X4547,X4548)
| c_Orderings_Oord__class_Oless__eq(X4550,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4550),X4549),X4548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4550),X4549),X4547))
| ~ c_Orderings_Oord__class_Oless(X4550,X4549,c_Groups_Ozero__class_Ozero(X4550))
| ~ class_Rings_Olinordered__ring__strict(X4550) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).
fof(i_0_1623,plain,
! [X3979] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk45_0,X3979)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X3979)),v_z____)),v_d____) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])]) ).
fof(i_0_1624,plain,
! [X3977] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk44_0,X3977)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X3977)),v_z____)),v_d____) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096])])]) ).
fof(i_0_1625,plain,
! [X3939] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,X3939)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X3939)),v_z____)),v_d____) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_N1])]) ).
fof(i_0_1626,plain,
! [X5148,X5149,X5150,X5151] :
( ( ~ c_Orderings_Oord__class_Oless(X5151,hAPP(hAPP(c_Power_Opower__class_Opower(X5151),X5150),X5149),hAPP(hAPP(c_Power_Opower__class_Opower(X5151),X5150),X5148))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5149,X5148)
| ~ c_Orderings_Oord__class_Oless(X5151,c_Groups_Oone__class_Oone(X5151),X5150)
| ~ class_Rings_Olinordered__semidom(X5151) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5149,X5148)
| c_Orderings_Oord__class_Oless(X5151,hAPP(hAPP(c_Power_Opower__class_Opower(X5151),X5150),X5149),hAPP(hAPP(c_Power_Opower__class_Opower(X5151),X5150),X5148))
| ~ c_Orderings_Oord__class_Oless(X5151,c_Groups_Oone__class_Oone(X5151),X5150)
| ~ class_Rings_Olinordered__semidom(X5151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_1627,plain,
! [X5144,X5145,X5146,X5147] :
( ~ class_Rings_Olinordered__semidom(X5147)
| ~ c_Orderings_Oord__class_Oless(X5147,c_Groups_Oone__class_Oone(X5147),X5146)
| ~ c_Orderings_Oord__class_Oless(X5147,hAPP(hAPP(c_Power_Opower__class_Opower(X5147),X5146),X5145),hAPP(hAPP(c_Power_Opower__class_Opower(X5147),X5146),X5144))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5145,X5144) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_1628,plain,
! [X5178,X5179,X5180,X5181] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5181,hAPP(hAPP(c_Power_Opower__class_Opower(X5181),X5180),X5179),hAPP(hAPP(c_Power_Opower__class_Opower(X5181),X5180),X5178))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5179,X5178)
| ~ c_Orderings_Oord__class_Oless(X5181,c_Groups_Oone__class_Oone(X5181),X5180)
| ~ class_Rings_Olinordered__semidom(X5181) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5179,X5178)
| c_Orderings_Oord__class_Oless__eq(X5181,hAPP(hAPP(c_Power_Opower__class_Opower(X5181),X5180),X5179),hAPP(hAPP(c_Power_Opower__class_Opower(X5181),X5180),X5178))
| ~ c_Orderings_Oord__class_Oless(X5181,c_Groups_Oone__class_Oone(X5181),X5180)
| ~ class_Rings_Olinordered__semidom(X5181) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).
fof(i_0_1629,plain,
! [X5174,X5175,X5176,X5177] :
( ~ class_Rings_Olinordered__semidom(X5177)
| ~ c_Orderings_Oord__class_Oless(X5177,c_Groups_Oone__class_Oone(X5177),X5176)
| ~ c_Orderings_Oord__class_Oless__eq(X5177,hAPP(hAPP(c_Power_Opower__class_Opower(X5177),X5176),X5175),hAPP(hAPP(c_Power_Opower__class_Opower(X5177),X5176),X5174))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5175,X5174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).
fof(i_0_1630,plain,
! [X3989,X3990,X3991] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3991))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3991),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3990),X3989)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3990),X3989) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3990))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3991),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3990),X3989)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3991),X3989)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3991)) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3990))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3991),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3990),X3989)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3991,X3990)),X3989)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3991)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1315])])]) ).
cnf(i_0_1631,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1316]) ).
cnf(i_0_1632,plain,
c_Int_Opred(X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_1317]) ).
cnf(i_0_1633,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(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_1318]) ).
cnf(i_0_1634,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),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_1319]) ).
fof(i_0_1635,plain,
! [X3696,X3697] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3697),X3696)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3696,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3697),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatceiling(X3696) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3697,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__eq])]) ).
fof(i_0_1636,plain,
! [X4483,X4484,X4485] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4485),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4484),X4483)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4485,X4484)),X4483),
inference(variable_rename,[status(thm)],[fact_zadd__int__left]) ).
fof(i_0_1637,plain,
! [X4765,X4766] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4766)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4765)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X4766)),c_RComplete_Onatfloor(X4765)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4766),X4765))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mult__natfloor])]) ).
fof(i_0_1638,plain,
! [X3691,X3692,X3693,X3694,X3695] :
( ~ class_Groups_Oab__group__add(X3695)
| c_Groups_Ominus__class_Ominus(X3695,c_Groups_Oplus__class_Oplus(X3695,X3694,X3693),c_Groups_Oplus__class_Oplus(X3695,X3692,X3691)) = c_Groups_Oplus__class_Oplus(X3695,c_Groups_Ominus__class_Ominus(X3695,X3694,X3692),c_Groups_Ominus__class_Ominus(X3695,X3693,X3691)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add])]) ).
fof(i_0_1639,plain,
! [X3034,X3035,X3036,X3037,X3038] :
( ~ class_Rings_Ocomm__semiring__1(X3038)
| c_Groups_Oplus__class_Oplus(X3038,c_Groups_Oplus__class_Oplus(X3038,X3037,X3036),c_Groups_Oplus__class_Oplus(X3038,X3035,X3034)) = c_Groups_Oplus__class_Oplus(X3038,c_Groups_Oplus__class_Oplus(X3038,X3037,X3035),c_Groups_Oplus__class_Oplus(X3038,X3036,X3034)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_1640,plain,
! [X5162,X5163,X5164,X5165] :
( ~ class_Rings_Olinordered__semidom(X5165)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5164,X5163)
| ~ c_Orderings_Oord__class_Oless(X5165,c_Groups_Ozero__class_Ozero(X5165),X5162)
| ~ c_Orderings_Oord__class_Oless(X5165,X5162,c_Groups_Oone__class_Oone(X5165))
| c_Orderings_Oord__class_Oless(X5165,hAPP(hAPP(c_Power_Opower__class_Opower(X5165),X5162),X5163),hAPP(hAPP(c_Power_Opower__class_Opower(X5165),X5162),X5164)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_1641,plain,
! [X5170,X5171,X5172,X5173] :
( ~ class_Rings_Olinordered__semidom(X5173)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5172,X5171)
| ~ c_Orderings_Oord__class_Oless__eq(X5173,c_Groups_Ozero__class_Ozero(X5173),X5170)
| ~ c_Orderings_Oord__class_Oless__eq(X5173,X5170,c_Groups_Oone__class_Oone(X5173))
| c_Orderings_Oord__class_Oless__eq(X5173,hAPP(hAPP(c_Power_Opower__class_Opower(X5173),X5170),X5171),hAPP(hAPP(c_Power_Opower__class_Opower(X5173),X5170),X5172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).
fof(i_0_1642,plain,
! [X5246,X5247,X5248,X5249] :
( ~ class_Divides_Osemiring__div(X5249)
| X5248 = c_Groups_Ozero__class_Ozero(X5249)
| c_Divides_Odiv__class_Odiv(X5249,c_Groups_Oplus__class_Oplus(X5249,X5247,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5249),X5248),X5246)),X5248) = c_Groups_Oplus__class_Oplus(X5249,X5246,c_Divides_Odiv__class_Odiv(X5249,X5247,X5248)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])]) ).
fof(i_0_1643,plain,
! [X5242,X5243,X5244,X5245] :
( ~ class_Divides_Osemiring__div(X5245)
| X5244 = c_Groups_Ozero__class_Ozero(X5245)
| c_Divides_Odiv__class_Odiv(X5245,c_Groups_Oplus__class_Oplus(X5245,X5243,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5245),X5242),X5244)),X5244) = c_Groups_Oplus__class_Oplus(X5245,X5242,c_Divides_Odiv__class_Odiv(X5245,X5243,X5244)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1])]) ).
fof(i_0_1644,plain,
! [X5010,X5011,X5012,X5013] :
( ~ class_Rings_Olinordered__semidom(X5013)
| ~ c_Orderings_Oord__class_Oless(X5013,X5012,X5011)
| ~ c_Orderings_Oord__class_Oless__eq(X5013,c_Groups_Ozero__class_Ozero(X5013),X5012)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5010)
| c_Orderings_Oord__class_Oless(X5013,hAPP(hAPP(c_Power_Opower__class_Opower(X5013),X5012),X5010),hAPP(hAPP(c_Power_Opower__class_Opower(X5013),X5011),X5010)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).
fof(i_0_1645,plain,
! [X5378,X5379,X5380,X5381] :
( ~ class_Fields_Ofield(X5381)
| X5380 = c_Groups_Ozero__class_Ozero(X5381)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5381),c_Rings_Oinverse__class_Odivide(X5381,X5379,X5380)),X5378) = c_Rings_Oinverse__class_Odivide(X5381,hAPP(hAPP(c_Power_Opower__class_Opower(X5381),X5379),X5378),hAPP(hAPP(c_Power_Opower__class_Opower(X5381),X5380),X5378)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).
cnf(i_0_1646,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Nat_OSuc(X3)))
| X3 != c_Divides_Odiv__class_Odiv(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_1289]) ).
fof(i_0_1647,plain,
! [X4377,X4378,X4379,X4380] :
( ( c_Orderings_Oord__class_Oless(X4380,X4379,c_Groups_Ozero__class_Ozero(X4380))
| c_Orderings_Oord__class_Oless(X4380,c_Groups_Ozero__class_Ozero(X4380),X4379)
| ~ c_Orderings_Oord__class_Oless(X4380,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4377))
| ~ class_Rings_Olinordered__ring__strict(X4380) )
& ( c_Orderings_Oord__class_Oless(X4380,X4377,X4378)
| c_Orderings_Oord__class_Oless(X4380,c_Groups_Ozero__class_Ozero(X4380),X4379)
| ~ c_Orderings_Oord__class_Oless(X4380,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4377))
| ~ class_Rings_Olinordered__ring__strict(X4380) )
& ( c_Orderings_Oord__class_Oless(X4380,X4379,c_Groups_Ozero__class_Ozero(X4380))
| c_Orderings_Oord__class_Oless(X4380,X4378,X4377)
| ~ c_Orderings_Oord__class_Oless(X4380,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4377))
| ~ class_Rings_Olinordered__ring__strict(X4380) )
& ( c_Orderings_Oord__class_Oless(X4380,X4377,X4378)
| c_Orderings_Oord__class_Oless(X4380,X4378,X4377)
| ~ c_Orderings_Oord__class_Oless(X4380,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4377))
| ~ class_Rings_Olinordered__ring__strict(X4380) )
& ( ~ c_Orderings_Oord__class_Oless(X4380,c_Groups_Ozero__class_Ozero(X4380),X4379)
| ~ c_Orderings_Oord__class_Oless(X4380,X4378,X4377)
| c_Orderings_Oord__class_Oless(X4380,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4377))
| ~ class_Rings_Olinordered__ring__strict(X4380) )
& ( ~ c_Orderings_Oord__class_Oless(X4380,X4379,c_Groups_Ozero__class_Ozero(X4380))
| ~ c_Orderings_Oord__class_Oless(X4380,X4377,X4378)
| c_Orderings_Oord__class_Oless(X4380,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),X4379),X4377))
| ~ class_Rings_Olinordered__ring__strict(X4380) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).
fof(i_0_1648,plain,
! [X4373,X4374,X4375,X4376] :
( ( c_Orderings_Oord__class_Oless(X4376,X4374,c_Groups_Ozero__class_Ozero(X4376))
| c_Orderings_Oord__class_Oless(X4376,c_Groups_Ozero__class_Ozero(X4376),X4374)
| ~ c_Orderings_Oord__class_Oless(X4376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4375),X4374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4373),X4374))
| ~ class_Rings_Olinordered__ring__strict(X4376) )
& ( c_Orderings_Oord__class_Oless(X4376,X4373,X4375)
| c_Orderings_Oord__class_Oless(X4376,c_Groups_Ozero__class_Ozero(X4376),X4374)
| ~ c_Orderings_Oord__class_Oless(X4376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4375),X4374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4373),X4374))
| ~ class_Rings_Olinordered__ring__strict(X4376) )
& ( c_Orderings_Oord__class_Oless(X4376,X4374,c_Groups_Ozero__class_Ozero(X4376))
| c_Orderings_Oord__class_Oless(X4376,X4375,X4373)
| ~ c_Orderings_Oord__class_Oless(X4376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4375),X4374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4373),X4374))
| ~ class_Rings_Olinordered__ring__strict(X4376) )
& ( c_Orderings_Oord__class_Oless(X4376,X4373,X4375)
| c_Orderings_Oord__class_Oless(X4376,X4375,X4373)
| ~ c_Orderings_Oord__class_Oless(X4376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4375),X4374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4373),X4374))
| ~ class_Rings_Olinordered__ring__strict(X4376) )
& ( ~ c_Orderings_Oord__class_Oless(X4376,c_Groups_Ozero__class_Ozero(X4376),X4374)
| ~ c_Orderings_Oord__class_Oless(X4376,X4375,X4373)
| c_Orderings_Oord__class_Oless(X4376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4375),X4374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4373),X4374))
| ~ class_Rings_Olinordered__ring__strict(X4376) )
& ( ~ c_Orderings_Oord__class_Oless(X4376,X4374,c_Groups_Ozero__class_Ozero(X4376))
| ~ c_Orderings_Oord__class_Oless(X4376,X4373,X4375)
| c_Orderings_Oord__class_Oless(X4376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4375),X4374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4373),X4374))
| ~ class_Rings_Olinordered__ring__strict(X4376) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).
fof(i_0_1649,plain,
! [X4948,X4949,X4951] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk68_2(X4948,X4949))
| ~ class_RealVector_Oreal__normed__algebra(X4949) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4949,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4949),X4951),X4948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4949,X4951)),esk68_2(X4948,X4949)))
| ~ class_RealVector_Oreal__normed__algebra(X4949) ) ),
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_1650,plain,
! [X4920,X4921,X4923] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk61_2(X4920,X4921))
| ~ class_RealVector_Oreal__normed__algebra(X4921) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4921,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4921),X4923),X4920)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4921,X4923)),esk61_2(X4920,X4921)))
| ~ class_RealVector_Oreal__normed__algebra(X4921) ) ),
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_1651,plain,
! [X4249,X4250,X4251] :
( ~ class_RealVector_Oreal__normed__algebra(X4251)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4251,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4251),X4250),X4249)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4251,X4250)),c_RealVector_Onorm__class_Onorm(X4251,X4249))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])]) ).
fof(i_0_1652,plain,
! [X4952,X4953,X4955] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk69_2(X4952,X4953))
| ~ class_RealVector_Oreal__normed__algebra(X4953) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4953,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4953),X4952),X4955)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4953,X4955)),esk69_2(X4952,X4953)))
| ~ class_RealVector_Oreal__normed__algebra(X4953) ) ),
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_1653,plain,
! [X4928,X4929,X4931] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk63_2(X4928,X4929))
| ~ class_RealVector_Oreal__normed__algebra(X4929) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4929,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4929),X4928),X4931)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4929,X4931)),esk63_2(X4928,X4929)))
| ~ class_RealVector_Oreal__normed__algebra(X4929) ) ),
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_1654,plain,
! [X3785,X3786,X3787,X3788] :
( ~ class_Int_Onumber__ring(X3788)
| c_Groups_Oplus__class_Oplus(X3788,c_Int_Onumber__class_Onumber__of(X3788,X3787),c_Groups_Ominus__class_Ominus(X3788,c_Int_Onumber__class_Onumber__of(X3788,X3786),X3785)) = c_Groups_Ominus__class_Ominus(X3788,c_Int_Onumber__class_Onumber__of(X3788,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3787,X3786)),X3785) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1])]) ).
fof(i_0_1655,plain,
! [X3735,X3736,X3737,X3738] :
( ~ class_Int_Onumber__ring(X3738)
| c_Groups_Oplus__class_Oplus(X3738,c_Int_Onumber__class_Onumber__of(X3738,X3737),c_Groups_Oplus__class_Oplus(X3738,c_Int_Onumber__class_Onumber__of(X3738,X3736),X3735)) = c_Groups_Oplus__class_Oplus(X3738,c_Int_Onumber__class_Onumber__of(X3738,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3737,X3736)),X3735) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).
cnf(i_0_1656,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1320]) ).
fof(i_0_1657,plain,
! [X4167,X4168,X4169,X4170] :
( ~ class_Rings_Ocomm__semiring__1(X4170)
| c_Groups_Oplus__class_Oplus(X4170,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4170),X4169),X4168),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4170),X4167),X4168)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4170),c_Groups_Oplus__class_Oplus(X4170,X4169,X4167)),X4168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).
fof(i_0_1658,plain,
! [X4256,X4257,X4258,X4259] :
( ~ class_RealVector_Oreal__normed__algebra(X4259)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4259),c_Groups_Ominus__class_Ominus(X4259,X4258,X4257)),X4256) = c_Groups_Ominus__class_Ominus(X4259,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4259),X4258),X4256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4259),X4257),X4256)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left])]) ).
fof(i_0_1659,plain,
! [X4252,X4253,X4254,X4255] :
( ~ class_RealVector_Oreal__normed__algebra(X4255)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4255),c_Groups_Ominus__class_Ominus(X4255,X4254,X4253)),X4252) = c_Groups_Ominus__class_Ominus(X4255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4255),X4254),X4252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4255),X4253),X4252)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff])]) ).
fof(i_0_1660,plain,
! [X4158,X4159,X4160,X4161] :
( ~ class_Rings_Ocomm__semiring(X4161)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4161),c_Groups_Oplus__class_Oplus(X4161,X4160,X4159)),X4158) = c_Groups_Oplus__class_Oplus(X4161,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4161),X4160),X4158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4161),X4159),X4158)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_1661,plain,
! [X4143,X4144,X4145,X4146] :
( ~ class_RealVector_Oreal__normed__algebra(X4146)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4146),c_Groups_Oplus__class_Oplus(X4146,X4145,X4144)),X4143) = c_Groups_Oplus__class_Oplus(X4146,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4146),X4145),X4143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4146),X4144),X4143)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).
fof(i_0_1662,plain,
! [X4139,X4140,X4141,X4142] :
( ~ class_RealVector_Oreal__normed__algebra(X4142)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4142),c_Groups_Oplus__class_Oplus(X4142,X4141,X4140)),X4139) = c_Groups_Oplus__class_Oplus(X4142,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4142),X4141),X4139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4142),X4140),X4139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).
fof(i_0_1663,plain,
! [X4171,X4172,X4173,X4174] :
( ~ class_Rings_Ocomm__semiring__1(X4174)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4174),c_Groups_Oplus__class_Oplus(X4174,X4173,X4172)),X4171) = c_Groups_Oplus__class_Oplus(X4174,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4174),X4173),X4171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4174),X4172),X4171)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
cnf(i_0_1664,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X1)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1321]) ).
cnf(i_0_1665,plain,
c_Int_Osucc(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_1322]) ).
cnf(i_0_1666,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_1323]) ).
fof(i_0_1667,plain,
! [X5376,X5377] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5377,X5376)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5377),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5376))),
inference(variable_rename,[status(thm)],[fact_real__of__nat__div4]) ).
fof(i_0_1668,plain,
! [X5226,X5227,X5228] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5228)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5227)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5227,X5226)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5228,X5226),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5228,X5227)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).
fof(i_0_1669,plain,
! [X5215,X5216,X5217] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5217,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5216)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5216,X5215)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5217,X5216),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5217,X5215)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).
fof(i_0_1670,plain,
! [X4970,X4971,X4972,X4973] :
( ~ class_Rings_Ocomm__semiring__1(X4973)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4973),hAPP(hAPP(c_Power_Opower__class_Opower(X4973),X4972),X4971)),hAPP(hAPP(c_Power_Opower__class_Opower(X4973),X4972),X4970)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4973),X4972),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4971,X4970)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).
fof(i_0_1671,plain,
! [X5110,X5111,X5112,X5113] :
( ~ class_Groups_Omonoid__mult(X5113)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5113),X5112),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5111,X5110)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5113),hAPP(hAPP(c_Power_Opower__class_Opower(X5113),X5112),X5111)),hAPP(hAPP(c_Power_Opower__class_Opower(X5113),X5112),X5110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_1672,plain,
! [X4214,X4215,X4216,X4217] :
( ~ class_Rings_Ocomm__semiring__1(X4217)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4217),X4216),X4215)),X4214) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4217),X4216),X4214)),X4215) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
cnf(i_0_1673,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk47_2(X2,X1))))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1284]) ).
cnf(i_0_1674,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(esk49_2(X2,X1))))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1285]) ).
fof(i_0_1675,plain,
! [X3772,X3773,X3774] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3774)
| c_Orderings_Oord__class_Oless__eq(X3774,c_Groups_Ominus__class_Ominus(X3774,c_Groups_Oabs__class_Oabs(X3774,X3773),c_Groups_Oabs__class_Oabs(X3774,X3772)),c_Groups_Oabs__class_Oabs(X3774,c_Groups_Ominus__class_Ominus(X3774,X3773,X3772))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).
fof(i_0_1676,plain,
! [X3775,X3776,X3777] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3777)
| c_Orderings_Oord__class_Oless__eq(X3777,c_Groups_Ominus__class_Ominus(X3777,c_Groups_Oabs__class_Oabs(X3777,X3776),c_Groups_Oabs__class_Oabs(X3777,X3775)),c_Groups_Oabs__class_Oabs(X3777,c_Groups_Ominus__class_Ominus(X3777,X3775,X3776))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])]) ).
fof(i_0_1677,plain,
! [X3795,X3796,X3797] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3797)
| c_Orderings_Oord__class_Oless__eq(X3797,c_Groups_Oabs__class_Oabs(X3797,c_Groups_Ominus__class_Ominus(X3797,X3796,X3795)),c_Groups_Oplus__class_Oplus(X3797,c_Groups_Oabs__class_Oabs(X3797,X3796),c_Groups_Oabs__class_Oabs(X3797,X3795))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).
fof(i_0_1678,plain,
! [X3766,X3767,X3768] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3768)
| c_Orderings_Oord__class_Oless__eq(X3768,c_Groups_Oabs__class_Oabs(X3768,c_Groups_Oplus__class_Oplus(X3768,X3767,X3766)),c_Groups_Oplus__class_Oplus(X3768,c_Groups_Oabs__class_Oabs(X3768,X3767),c_Groups_Oabs__class_Oabs(X3768,X3766))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).
fof(i_0_1679,plain,
! [X4448,X4449,X4450,X4451,X4452,X4453] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4453)
| X4452 = c_Groups_Ozero__class_Ozero(X4453)
| X4451 != X4450
| X4449 = X4448
| c_Groups_Oplus__class_Oplus(X4453,X4451,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4453),X4452),X4449)) != c_Groups_Oplus__class_Oplus(X4453,X4450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4453),X4452),X4448)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
fof(i_0_1680,plain,
! [X4788,X4789,X4790] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4789),X4790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4788),X4790))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4789,X4788)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4790) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4789,X4788)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4789),X4790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4788),X4790))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4790) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1])])]) ).
fof(i_0_1681,plain,
! [X5028,X5029,X5030] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5030)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5030),X5029),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5030),X5028))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5029,X5028) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_1682,plain,
! [X4880,X4881,X4882] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4882),X4881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4882),X4880))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4881,X4880)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4882) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4881,X4880)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4882),X4881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4882),X4880))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4882) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_1683,plain,
! [X4816,X4817,X4818] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4817),X4818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4816),X4818))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4817,X4816)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4818) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4817,X4816)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4817),X4818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4816),X4818))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4818) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1])])]) ).
fof(i_0_1684,plain,
! [X4813,X4814,X4815] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4815),X4814),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4815),X4813))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4814,X4813)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4815) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4814,X4813)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4815),X4814),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4815),X4813))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4815) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2])])]) ).
fof(i_0_1685,plain,
! [X4821,X4822,X4823] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4823),X4822),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4821),X4822))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4822)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4823,X4821) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4822)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4823),X4822),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4821),X4822)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4823,X4821)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4823),X4822),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4821),X4822)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).
fof(i_0_1686,plain,
! [X4886,X4887,X4888] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4888),X4887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4888),X4886))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4887,X4886)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4888) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4887,X4886)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4888),X4887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4888),X4886))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4888) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).
fof(i_0_1687,plain,
! [X4824,X4825,X4826] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4826),X4825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4826),X4824))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4826)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4825,X4824) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4826)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4826),X4825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4826),X4824)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4825,X4824)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4826),X4825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4826),X4824)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).
fof(i_0_1688,plain,
! [X3930,X3931,X3932] :
( ~ class_RealVector_Oreal__normed__vector(X3932)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3932,X3931),c_RealVector_Onorm__class_Onorm(X3932,X3930)),c_RealVector_Onorm__class_Onorm(X3932,c_Groups_Ominus__class_Ominus(X3932,X3931,X3930))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2])]) ).
fof(i_0_1689,plain,
! [X3933,X3934,X3935] :
( ~ class_RealVector_Oreal__normed__vector(X3935)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3935,X3934),c_RealVector_Onorm__class_Onorm(X3935,X3933)),c_RealVector_Onorm__class_Onorm(X3935,c_Groups_Oplus__class_Oplus(X3935,X3934,X3933))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq])]) ).
fof(i_0_1690,plain,
! [X3936,X3937,X3938] :
( ~ class_RealVector_Oreal__normed__vector(X3938)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3938,c_Groups_Ominus__class_Ominus(X3938,X3937,X3936)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3938,X3937),c_RealVector_Onorm__class_Onorm(X3938,X3936))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq4])]) ).
fof(i_0_1691,plain,
! [X3961,X3962,X3963] :
( ~ class_RealVector_Oreal__normed__vector(X3963)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3963,c_Groups_Oplus__class_Oplus(X3963,X3962,X3961)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3963,X3962),c_RealVector_Onorm__class_Onorm(X3963,X3961))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq])]) ).
fof(i_0_1692,plain,
! [X3920,X3921] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3921),X3920)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3920,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3921),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatfloor(X3920) = X3921 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__eq])]) ).
cnf(i_0_1693,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(esk60_2(X2,X1))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1320]) ).
fof(i_0_1694,plain,
! [X3578,X3579,X3580] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3578,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3579,X3580))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3578,X3580),X3579)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3580,X3579) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3578,X3580),X3579)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3578,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3579,X3580))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3580,X3579) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).
fof(i_0_1695,plain,
! [X4238,X4239,X4240] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4240,X4239)),X4238) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4240),X4238),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4239),X4238)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).
fof(i_0_1696,plain,
! [X4147,X4148,X4149] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4149,X4148)),X4147) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4149),X4147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4148),X4147)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_1697,plain,
! [X4712,X4713,X4714] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4714,X4713)),X4712) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4714),X4712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4713),X4712)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
fof(i_0_1698,plain,
! [X4748,X4749,X4750] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4750,X4749)),X4748) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4750),X4748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4749),X4748)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).
fof(i_0_1699,plain,
! [X4706,X4707,X4708] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4708,X4707)),X4706) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4708),X4706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4707),X4706)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
cnf(i_0_1700,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_1324]) ).
fof(i_0_1701,plain,
! [X4965,X4966,X4967] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4967)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4967,hAPP(hAPP(c_Power_Opower__class_Opower(X4967),X4966),X4965)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4967,X4966)),X4965)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power__ineq])]) ).
fof(i_0_1702,plain,
! [X3398,X3399,X3400,X3401] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3401)
| ~ c_Orderings_Oord__class_Oless(X3401,c_Groups_Oplus__class_Oplus(X3401,X3400,X3399),c_Groups_Oplus__class_Oplus(X3401,X3398,X3399))
| c_Orderings_Oord__class_Oless(X3401,X3400,X3398) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_1703,plain,
! [X3377,X3378,X3379,X3380] :
( ( ~ c_Orderings_Oord__class_Oless(X3380,c_Groups_Oplus__class_Oplus(X3380,X3379,X3378),c_Groups_Oplus__class_Oplus(X3380,X3377,X3378))
| c_Orderings_Oord__class_Oless(X3380,X3379,X3377)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3380) )
& ( ~ c_Orderings_Oord__class_Oless(X3380,X3379,X3377)
| c_Orderings_Oord__class_Oless(X3380,c_Groups_Oplus__class_Oplus(X3380,X3379,X3378),c_Groups_Oplus__class_Oplus(X3380,X3377,X3378))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3380) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_1704,plain,
! [X3402,X3403,X3404,X3405] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3405)
| ~ c_Orderings_Oord__class_Oless(X3405,c_Groups_Oplus__class_Oplus(X3405,X3404,X3403),c_Groups_Oplus__class_Oplus(X3405,X3404,X3402))
| c_Orderings_Oord__class_Oless(X3405,X3403,X3402) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_1705,plain,
! [X3381,X3382,X3383,X3384] :
( ( ~ c_Orderings_Oord__class_Oless(X3384,c_Groups_Oplus__class_Oplus(X3384,X3383,X3382),c_Groups_Oplus__class_Oplus(X3384,X3383,X3381))
| c_Orderings_Oord__class_Oless(X3384,X3382,X3381)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3384) )
& ( ~ c_Orderings_Oord__class_Oless(X3384,X3382,X3381)
| c_Orderings_Oord__class_Oless(X3384,c_Groups_Oplus__class_Oplus(X3384,X3383,X3382),c_Groups_Oplus__class_Oplus(X3384,X3383,X3381))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3384) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_1706,plain,
! [X2773,X2774,X2775,X2776] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2776)
| ~ c_Orderings_Oord__class_Oless__eq(X2776,c_Groups_Oplus__class_Oplus(X2776,X2775,X2774),c_Groups_Oplus__class_Oplus(X2776,X2773,X2774))
| c_Orderings_Oord__class_Oless__eq(X2776,X2775,X2773) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_1707,plain,
! [X2752,X2753,X2754,X2755] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2755,c_Groups_Oplus__class_Oplus(X2755,X2754,X2753),c_Groups_Oplus__class_Oplus(X2755,X2752,X2753))
| c_Orderings_Oord__class_Oless__eq(X2755,X2754,X2752)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2755) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2755,X2754,X2752)
| c_Orderings_Oord__class_Oless__eq(X2755,c_Groups_Oplus__class_Oplus(X2755,X2754,X2753),c_Groups_Oplus__class_Oplus(X2755,X2752,X2753))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2755) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_1708,plain,
! [X2777,X2778,X2779,X2780] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2780)
| ~ c_Orderings_Oord__class_Oless__eq(X2780,c_Groups_Oplus__class_Oplus(X2780,X2779,X2778),c_Groups_Oplus__class_Oplus(X2780,X2779,X2777))
| c_Orderings_Oord__class_Oless__eq(X2780,X2778,X2777) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_1709,plain,
! [X2756,X2757,X2758,X2759] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2759,c_Groups_Oplus__class_Oplus(X2759,X2758,X2757),c_Groups_Oplus__class_Oplus(X2759,X2758,X2756))
| c_Orderings_Oord__class_Oless__eq(X2759,X2757,X2756)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2759) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2759,X2757,X2756)
| c_Orderings_Oord__class_Oless__eq(X2759,c_Groups_Oplus__class_Oplus(X2759,X2758,X2757),c_Groups_Oplus__class_Oplus(X2759,X2758,X2756))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2759) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
cnf(i_0_1710,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_1325]) ).
cnf(i_0_1711,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_1326]) ).
cnf(i_0_1712,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_1327]) ).
cnf(i_0_1713,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_1328]) ).
fof(i_0_1714,plain,
! [X3427,X3428,X3429] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3429,X3428)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3429,X3427)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3428,X3429),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3427,X3429)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3428,X3427) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).
fof(i_0_1715,plain,
! [X5129,X5130,X5131] :
( ~ class_Rings_Olinordered__semidom(X5131)
| ~ c_Orderings_Oord__class_Oless(X5131,c_Groups_Oone__class_Oone(X5131),X5130)
| c_Orderings_Oord__class_Oless(X5131,c_Groups_Oone__class_Oone(X5131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5131),X5130),hAPP(hAPP(c_Power_Opower__class_Opower(X5131),X5130),X5129))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).
fof(i_0_1716,plain,
! [X5038,X5039,X5040] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5040),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5039,X5038)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5040),X5039)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5040),X5038)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
cnf(i_0_1717,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_1329]) ).
fof(i_0_1718,plain,
! [X3480,X3481,X3482] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3482,X3481),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3482,X3480))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3481,X3480) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3481,X3480)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3482,X3481),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3482,X3480)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_1719,plain,
! [X2826,X2827,X2828] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2828,X2827),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2828,X2826))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2827,X2826) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2827,X2826)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2828,X2827),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2828,X2826)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_1720,plain,
! [X3044,X3045] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3045,X3044)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3045),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3044)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3045),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3044))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3045,X3044) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__real__le])]) ).
fof(i_0_1721,plain,
! [X3042,X3043] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3043,X3042)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3043),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3042),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3043),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3042),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3043,X3042) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__real__less])]) ).
fof(i_0_1722,plain,
! [X4678,X4679,X4680] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4680)
| X4680 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4680),X4678))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4679)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4678,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_1723,plain,
! [X4681,X4682,X4683] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4683)
| X4683 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4683),X4681))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4682,X4683)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4681) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).
fof(i_0_1724,plain,
! [X5166,X5167,X5168,X5169] :
( ~ class_Rings_Olinordered__semidom(X5169)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5169),X5168),X5167) != hAPP(hAPP(c_Power_Opower__class_Opower(X5169),X5166),X5167)
| ~ c_Orderings_Oord__class_Oless__eq(X5169,c_Groups_Ozero__class_Ozero(X5169),X5168)
| ~ c_Orderings_Oord__class_Oless__eq(X5169,c_Groups_Ozero__class_Ozero(X5169),X5166)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5167)
| X5168 = X5166 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).
fof(i_0_1725,plain,
! [X4513,X4514,X4515] :
( ~ class_Rings_Ocomm__semiring__1(X4515)
| c_Groups_Oplus__class_Oplus(X4515,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4515),X4514),X4513),X4513) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4515),c_Groups_Oplus__class_Oplus(X4515,X4514,c_Groups_Oone__class_Oone(X4515))),X4513) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
fof(i_0_1726,plain,
! [X4510,X4511,X4512] :
( ~ class_Rings_Ocomm__semiring__1(X4512)
| c_Groups_Oplus__class_Oplus(X4512,X4511,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4512),X4510),X4511)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4512),c_Groups_Oplus__class_Oplus(X4512,X4510,c_Groups_Oone__class_Oone(X4512))),X4511) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
fof(i_0_1727,plain,
! [X4608,X4609,X4610] :
( ~ class_Rings_Olinordered__idom(X4610)
| ~ c_Orderings_Oord__class_Oless__eq(X4610,c_Groups_Ozero__class_Ozero(X4610),X4609)
| ~ c_Orderings_Oord__class_Oless__eq(X4610,c_Groups_Ozero__class_Ozero(X4610),X4608)
| ~ c_Orderings_Oord__class_Oless__eq(X4610,X4608,c_Groups_Oone__class_Oone(X4610))
| c_Orderings_Oord__class_Oless__eq(X4610,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4610),X4609),X4608),X4609) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).
fof(i_0_1728,plain,
! [X4611,X4612,X4613] :
( ~ class_Rings_Olinordered__idom(X4613)
| ~ c_Orderings_Oord__class_Oless__eq(X4613,c_Groups_Ozero__class_Ozero(X4613),X4612)
| ~ c_Orderings_Oord__class_Oless__eq(X4613,c_Groups_Ozero__class_Ozero(X4613),X4611)
| ~ c_Orderings_Oord__class_Oless__eq(X4613,X4611,c_Groups_Oone__class_Oone(X4613))
| c_Orderings_Oord__class_Oless__eq(X4613,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4613),X4611),X4612),X4612) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).
fof(i_0_1729,plain,
! [X4830,X4831,X4832,X4833] :
( ~ class_RealVector_Oreal__normed__vector(X4833)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4832,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4833,X4831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4832),c_RealVector_Onorm__class_Onorm(X4833,X4830)))
| X4831 = c_Groups_Ozero__class_Ozero(X4833) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ratiotest__lemma])]) ).
fof(i_0_1730,plain,
! [X4410,X4411,X4412,X4413] :
( ~ class_Rings_Olinordered__semiring__strict(X4413)
| ~ c_Orderings_Oord__class_Oless(X4413,X4412,X4411)
| ~ c_Orderings_Oord__class_Oless(X4413,c_Groups_Ozero__class_Ozero(X4413),X4410)
| c_Orderings_Oord__class_Oless(X4413,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4413),X4412),X4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4413),X4411),X4410)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_1731,plain,
! [X4418,X4419,X4420,X4421] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X4421)
| ~ c_Orderings_Oord__class_Oless(X4421,X4420,X4419)
| ~ c_Orderings_Oord__class_Oless(X4421,c_Groups_Ozero__class_Ozero(X4421),X4418)
| c_Orderings_Oord__class_Oless(X4421,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4421),X4418),X4420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4421),X4418),X4419)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_1732,plain,
! [X4414,X4415,X4416,X4417] :
( ~ class_Rings_Olinordered__semiring__strict(X4417)
| ~ c_Orderings_Oord__class_Oless(X4417,X4416,X4415)
| ~ c_Orderings_Oord__class_Oless(X4417,c_Groups_Ozero__class_Ozero(X4417),X4414)
| c_Orderings_Oord__class_Oless(X4417,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4417),X4414),X4416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4417),X4414),X4415)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_1733,plain,
! [X5083,X5084,X5085,X5086] :
( ~ class_Rings_Olinordered__semidom(X5086)
| ~ c_Orderings_Oord__class_Oless__eq(X5086,X5085,X5084)
| ~ c_Orderings_Oord__class_Oless__eq(X5086,c_Groups_Ozero__class_Ozero(X5086),X5085)
| c_Orderings_Oord__class_Oless__eq(X5086,hAPP(hAPP(c_Power_Opower__class_Opower(X5086),X5085),X5083),hAPP(hAPP(c_Power_Opower__class_Opower(X5086),X5084),X5083)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).
fof(i_0_1734,plain,
! [X4335,X4336,X4337,X4338] :
( ~ class_Rings_Oordered__semiring(X4338)
| ~ c_Orderings_Oord__class_Oless__eq(X4338,X4337,X4336)
| ~ c_Orderings_Oord__class_Oless__eq(X4338,c_Groups_Ozero__class_Ozero(X4338),X4335)
| c_Orderings_Oord__class_Oless__eq(X4338,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4338),X4337),X4335),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4338),X4336),X4335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).
fof(i_0_1735,plain,
! [X4343,X4344,X4345,X4346] :
( ~ class_Rings_Oordered__comm__semiring(X4346)
| ~ c_Orderings_Oord__class_Oless__eq(X4346,X4345,X4344)
| ~ c_Orderings_Oord__class_Oless__eq(X4346,c_Groups_Ozero__class_Ozero(X4346),X4343)
| c_Orderings_Oord__class_Oless__eq(X4346,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4346),X4343),X4345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4346),X4343),X4344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).
fof(i_0_1736,plain,
! [X4339,X4340,X4341,X4342] :
( ~ class_Rings_Oordered__semiring(X4342)
| ~ c_Orderings_Oord__class_Oless__eq(X4342,X4341,X4340)
| ~ c_Orderings_Oord__class_Oless__eq(X4342,c_Groups_Ozero__class_Ozero(X4342),X4339)
| c_Orderings_Oord__class_Oless__eq(X4342,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4342),X4339),X4341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4342),X4339),X4340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).
fof(i_0_1737,plain,
! [X4422,X4423,X4424,X4425] :
( ~ class_Rings_Olinordered__ring__strict(X4425)
| ~ c_Orderings_Oord__class_Oless(X4425,X4424,X4423)
| ~ c_Orderings_Oord__class_Oless(X4425,X4422,c_Groups_Ozero__class_Ozero(X4425))
| c_Orderings_Oord__class_Oless(X4425,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4425),X4423),X4422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4425),X4424),X4422)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_1738,plain,
! [X4426,X4427,X4428,X4429] :
( ~ class_Rings_Olinordered__ring__strict(X4429)
| ~ c_Orderings_Oord__class_Oless(X4429,X4428,X4427)
| ~ c_Orderings_Oord__class_Oless(X4429,X4426,c_Groups_Ozero__class_Ozero(X4429))
| c_Orderings_Oord__class_Oless(X4429,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4429),X4426),X4427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4429),X4426),X4428)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
fof(i_0_1739,plain,
! [X4347,X4348,X4349,X4350] :
( ~ class_Rings_Oordered__ring(X4350)
| ~ c_Orderings_Oord__class_Oless__eq(X4350,X4349,X4348)
| ~ c_Orderings_Oord__class_Oless__eq(X4350,X4347,c_Groups_Ozero__class_Ozero(X4350))
| c_Orderings_Oord__class_Oless__eq(X4350,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4350),X4348),X4347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4350),X4349),X4347)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).
fof(i_0_1740,plain,
! [X4351,X4352,X4353,X4354] :
( ~ class_Rings_Oordered__ring(X4354)
| ~ c_Orderings_Oord__class_Oless__eq(X4354,X4353,X4352)
| ~ c_Orderings_Oord__class_Oless__eq(X4354,X4351,c_Groups_Ozero__class_Ozero(X4354))
| c_Orderings_Oord__class_Oless__eq(X4354,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4354),X4351),X4352),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4354),X4351),X4353)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).
fof(i_0_1741,plain,
! [X3586,X3587,X3588] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3588,X3587)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3586,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3587,X3586),X3588)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).
fof(i_0_1742,plain,
! [X3393,X3394,X3395,X3396,X3397] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3397)
| ~ c_Orderings_Oord__class_Oless(X3397,X3396,X3395)
| ~ c_Orderings_Oord__class_Oless(X3397,X3394,X3393)
| c_Orderings_Oord__class_Oless(X3397,c_Groups_Oplus__class_Oplus(X3397,X3396,X3394),c_Groups_Oplus__class_Oplus(X3397,X3395,X3393)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_1743,plain,
! [X3557,X3558,X3559,X3560,X3561] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3561)
| ~ c_Orderings_Oord__class_Oless__eq(X3561,X3560,X3559)
| ~ c_Orderings_Oord__class_Oless(X3561,X3558,X3557)
| c_Orderings_Oord__class_Oless(X3561,c_Groups_Oplus__class_Oplus(X3561,X3560,X3558),c_Groups_Oplus__class_Oplus(X3561,X3559,X3557)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_1744,plain,
! [X3552,X3553,X3554,X3555,X3556] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3556)
| ~ c_Orderings_Oord__class_Oless(X3556,X3555,X3554)
| ~ c_Orderings_Oord__class_Oless__eq(X3556,X3553,X3552)
| c_Orderings_Oord__class_Oless(X3556,c_Groups_Oplus__class_Oplus(X3556,X3555,X3553),c_Groups_Oplus__class_Oplus(X3556,X3554,X3552)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_1745,plain,
! [X2768,X2769,X2770,X2771,X2772] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2772)
| ~ c_Orderings_Oord__class_Oless__eq(X2772,X2771,X2770)
| ~ c_Orderings_Oord__class_Oless__eq(X2772,X2769,X2768)
| c_Orderings_Oord__class_Oless__eq(X2772,c_Groups_Oplus__class_Oplus(X2772,X2771,X2769),c_Groups_Oplus__class_Oplus(X2772,X2770,X2768)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_1746,plain,
! [X5140,X5141,X5142,X5143] :
( ~ class_Rings_Olinordered__semidom(X5143)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5142,X5141)
| ~ c_Orderings_Oord__class_Oless(X5143,c_Groups_Oone__class_Oone(X5143),X5140)
| c_Orderings_Oord__class_Oless(X5143,hAPP(hAPP(c_Power_Opower__class_Opower(X5143),X5140),X5142),hAPP(hAPP(c_Power_Opower__class_Opower(X5143),X5140),X5141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_1747,plain,
! [X5152,X5153,X5154,X5155] :
( ~ class_Rings_Olinordered__semidom(X5155)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5154,X5153)
| ~ c_Orderings_Oord__class_Oless__eq(X5155,c_Groups_Oone__class_Oone(X5155),X5152)
| c_Orderings_Oord__class_Oless__eq(X5155,hAPP(hAPP(c_Power_Opower__class_Opower(X5155),X5152),X5154),hAPP(hAPP(c_Power_Opower__class_Opower(X5155),X5152),X5153)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).
fof(i_0_1748,plain,
! [X4647,X4648,X4649] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4649,c_Groups_Ozero__class_Ozero(X4649),X4647)
| ~ c_Orderings_Oord__class_Oless__eq(X4649,c_Groups_Ozero__class_Ozero(X4649),X4648)
| c_Groups_Oabs__class_Oabs(X4649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4649),X4648),X4647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4649),c_Groups_Oabs__class_Oabs(X4649,X4648)),c_Groups_Oabs__class_Oabs(X4649,X4647))
| ~ class_Rings_Oordered__ring__abs(X4649) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4649,X4647,c_Groups_Ozero__class_Ozero(X4649))
| ~ c_Orderings_Oord__class_Oless__eq(X4649,c_Groups_Ozero__class_Ozero(X4649),X4648)
| c_Groups_Oabs__class_Oabs(X4649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4649),X4648),X4647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4649),c_Groups_Oabs__class_Oabs(X4649,X4648)),c_Groups_Oabs__class_Oabs(X4649,X4647))
| ~ class_Rings_Oordered__ring__abs(X4649) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4649,c_Groups_Ozero__class_Ozero(X4649),X4647)
| ~ c_Orderings_Oord__class_Oless__eq(X4649,X4648,c_Groups_Ozero__class_Ozero(X4649))
| c_Groups_Oabs__class_Oabs(X4649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4649),X4648),X4647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4649),c_Groups_Oabs__class_Oabs(X4649,X4648)),c_Groups_Oabs__class_Oabs(X4649,X4647))
| ~ class_Rings_Oordered__ring__abs(X4649) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4649,X4647,c_Groups_Ozero__class_Ozero(X4649))
| ~ c_Orderings_Oord__class_Oless__eq(X4649,X4648,c_Groups_Ozero__class_Ozero(X4649))
| c_Groups_Oabs__class_Oabs(X4649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4649),X4648),X4647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4649),c_Groups_Oabs__class_Oabs(X4649,X4648)),c_Groups_Oabs__class_Oabs(X4649,X4647))
| ~ class_Rings_Oordered__ring__abs(X4649) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).
fof(i_0_1749,plain,
! [X3698,X3699,X3701] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk31_2(X3698,X3699),X3698)
| ~ hBOOL(hAPP(X3699,X3698))
| hBOOL(hAPP(X3699,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3701,esk31_2(X3698,X3699))
| ~ hBOOL(hAPP(X3699,X3701))
| ~ hBOOL(hAPP(X3699,X3698))
| hBOOL(hAPP(X3699,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X3699,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk31_2(X3698,X3699),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X3699,X3698))
| hBOOL(hAPP(X3699,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_1330])])])])]) ).
fof(i_0_1750,plain,
! [X5007,X5008,X5009] :
( ( X5008 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5009),X5007),X5008) = c_Groups_Oone__class_Oone(X5009)
| ~ class_Power_Opower(X5009) )
& ( X5008 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5009),X5007),X5008) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5009),X5007),hAPP(hAPP(c_Power_Opower__class_Opower(X5009),X5007),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5008,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X5009) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if])])]) ).
cnf(i_0_1751,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_1331]) ).
fof(i_0_1752,plain,
! [X5210,X5211,X5212] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5212,X5211)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5210)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5212,X5210),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5211,X5210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).
fof(i_0_1753,plain,
! [X5333,X5334,X5335] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5335)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5335,X5334)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5333,X5334),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5333,X5335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])]) ).
fof(i_0_1754,plain,
! [X5207,X5208,X5209] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5209,X5208)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5207,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,X5208,X5207),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5209,X5207)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).
fof(i_0_1755,plain,
! [X5296,X5297,X5298] :
( ( ~ hBOOL(hAPP(X5298,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5297,X5296)))
| epred1_3(X5298,X5296,X5297) )
& ( ~ epred1_3(X5298,X5296,X5297)
| hBOOL(hAPP(X5298,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5297,X5296))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1332])]) ).
fof(i_0_1756,plain,
! [X3841,X3842,X3843,X3844] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3844,X3843)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3842,X3841)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3844,X3842),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3843,X3841)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).
fof(i_0_1757,plain,
! [X3231,X3232,X3233] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3233,X3232)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3231,X3233)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3233,X3231),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3232,X3231)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).
fof(i_0_1758,plain,
! [X3206,X3207,X3208] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3208,X3207)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3208,X3206)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3206,X3207),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3206,X3208)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).
fof(i_0_1759,plain,
! [X3492,X3493,X3494,X3495] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3495,X3494)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3493,X3492)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3495,X3493),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3494,X3492)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_1760,plain,
! [X2813,X2814,X2815,X2816] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2816,X2815)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2814,X2813)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2816,X2814),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2815,X2813)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_1761,plain,
! [X4445,X4446,X4447] :
( ( X4446 = c_Groups_Ozero__class_Ozero(X4447)
| c_Groups_Oplus__class_Oplus(X4447,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4447),X4446),X4446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4447),X4445),X4445)) != c_Groups_Ozero__class_Ozero(X4447)
| ~ class_Rings_Olinordered__ring__strict(X4447) )
& ( X4445 = c_Groups_Ozero__class_Ozero(X4447)
| c_Groups_Oplus__class_Oplus(X4447,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4447),X4446),X4446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4447),X4445),X4445)) != c_Groups_Ozero__class_Ozero(X4447)
| ~ class_Rings_Olinordered__ring__strict(X4447) )
& ( X4446 != c_Groups_Ozero__class_Ozero(X4447)
| X4445 != c_Groups_Ozero__class_Ozero(X4447)
| c_Groups_Oplus__class_Oplus(X4447,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4447),X4446),X4446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4447),X4445),X4445)) = c_Groups_Ozero__class_Ozero(X4447)
| ~ class_Rings_Olinordered__ring__strict(X4447) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).
cnf(i_0_1762,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_1333]) ).
cnf(i_0_1763,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_1334]) ).
fof(i_0_1764,plain,
! [X4827,X4828,X4829] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4829,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4828),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4829),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4827)))
| X4828 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rabs__ratiotest__lemma])]) ).
fof(i_0_1765,plain,
! [X4264,X4265,X4266,X4267] :
( ~ class_RealVector_Oreal__normed__algebra(X4267)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4267),X4266),c_Groups_Ominus__class_Ominus(X4267,X4265,X4264)) = c_Groups_Ominus__class_Ominus(X4267,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4267),X4266),X4265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4267),X4266),X4264)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right])]) ).
fof(i_0_1766,plain,
! [X4260,X4261,X4262,X4263] :
( ~ class_RealVector_Oreal__normed__algebra(X4263)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4263),X4262),c_Groups_Ominus__class_Ominus(X4263,X4261,X4260)) = c_Groups_Ominus__class_Ominus(X4263,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4263),X4262),X4261),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4263),X4262),X4260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff])]) ).
fof(i_0_1767,plain,
! [X4135,X4136,X4137,X4138] :
( ~ class_RealVector_Oreal__normed__algebra(X4138)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4138),X4137),c_Groups_Oplus__class_Oplus(X4138,X4136,X4135)) = c_Groups_Oplus__class_Oplus(X4138,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4138),X4137),X4136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4138),X4137),X4135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).
fof(i_0_1768,plain,
! [X4131,X4132,X4133,X4134] :
( ~ class_RealVector_Oreal__normed__algebra(X4134)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4134),X4133),c_Groups_Oplus__class_Oplus(X4134,X4132,X4131)) = c_Groups_Oplus__class_Oplus(X4134,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4134),X4133),X4132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4134),X4133),X4131)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).
fof(i_0_1769,plain,
! [X4180,X4181,X4182,X4183] :
( ~ class_Rings_Ocomm__semiring__1(X4183)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4183),X4182),c_Groups_Oplus__class_Oplus(X4183,X4181,X4180)) = c_Groups_Oplus__class_Oplus(X4183,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4183),X4182),X4181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4183),X4182),X4180)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).
fof(i_0_1770,plain,
! [X4771,X4772,X4773] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4773)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4773),X4772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4773),X4771)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4772,X4771)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4773),X4772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4773),X4771)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4773)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4772,X4771)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4773),X4772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4773),X4771)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_1771,plain,
! [X4774,X4775,X4776] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4775)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4776),X4775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4774),X4775)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4776,X4774)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4776),X4775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4774),X4775)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4775)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4776,X4774)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4776),X4775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4774),X4775)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
fof(i_0_1772,plain,
! [X5229,X5230] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5229,X5230)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5230,X5229))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5230) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5229)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5230,X5229))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5230) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5229,X5230)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5229)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5230,X5229))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5230) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).
fof(i_0_1773,plain,
! [X4397,X4398,X4399] :
( ~ class_Rings_Olinordered__semiring__strict(X4399)
| ~ c_Orderings_Oord__class_Oless(X4399,c_Groups_Ozero__class_Ozero(X4399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4399),X4398),X4397))
| ~ c_Orderings_Oord__class_Oless(X4399,c_Groups_Ozero__class_Ozero(X4399),X4397)
| c_Orderings_Oord__class_Oless(X4399,c_Groups_Ozero__class_Ozero(X4399),X4398) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_1774,plain,
! [X4394,X4395,X4396] :
( ~ class_Rings_Olinordered__semiring__strict(X4396)
| ~ c_Orderings_Oord__class_Oless(X4396,c_Groups_Ozero__class_Ozero(X4396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4396),X4395),X4394))
| ~ c_Orderings_Oord__class_Oless(X4396,c_Groups_Ozero__class_Ozero(X4396),X4395)
| c_Orderings_Oord__class_Oless(X4396,c_Groups_Ozero__class_Ozero(X4396),X4394) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
fof(i_0_1775,plain,
! [X5299,X5300,X5301] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X5301,X5300)),X5299) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5301),X5299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5299)),X5300)),
inference(variable_rename,[status(thm)],[fact_DeMoivre2]) ).
fof(i_0_1776,plain,
! [X5059,X5060,X5061] :
( ~ class_Groups_Omonoid__mult(X5061)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5061),hAPP(hAPP(c_Power_Opower__class_Opower(X5061),X5060),X5059)),X5060) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5061),X5060),hAPP(hAPP(c_Power_Opower__class_Opower(X5061),X5060),X5059)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_1777,plain,
! [X4189,X4190,X4191,X4192] :
( ~ class_Groups_Oab__semigroup__mult(X4192)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4192),X4191),X4190)),X4189) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4192),X4191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4192),X4190),X4189)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_1778,plain,
! [X4218,X4219,X4220,X4221] :
( ~ class_Rings_Ocomm__semiring__1(X4221)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),X4219)),X4218) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4221),X4219),X4218)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_1779,plain,
! [X4222,X4223,X4224,X4225] :
( ~ class_Rings_Ocomm__semiring__1(X4225)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4223),X4222)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4225),X4224),X4223)),X4222) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).
fof(i_0_1780,plain,
! [X3809] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk32_1(X3809),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3809)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3809) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3809,hAPP(c_RealDef_Oreal(tc_Nat_Onat),esk32_1(X3809)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3809) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6])])])]) ).
cnf(i_0_1781,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(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_1335]) ).
fof(i_0_1782,plain,
! [X2992,X2993,X2994,X2995,X2996,X2997] :
( ( ~ c_SEQ_Omonoseq(X2993,X2992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2994,X2995)
| c_Orderings_Oord__class_Oless__eq(X2993,hAPP(X2992,X2994),hAPP(X2992,X2995))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2996,X2997)
| c_Orderings_Oord__class_Oless__eq(X2993,hAPP(X2992,X2997),hAPP(X2992,X2996))
| ~ class_Orderings_Oorder(X2993) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk10_2(X2992,X2993),esk11_2(X2992,X2993))
| c_SEQ_Omonoseq(X2993,X2992)
| ~ class_Orderings_Oorder(X2993) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2993,hAPP(X2992,esk10_2(X2992,X2993)),hAPP(X2992,esk11_2(X2992,X2993)))
| c_SEQ_Omonoseq(X2993,X2992)
| ~ class_Orderings_Oorder(X2993) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk12_2(X2992,X2993),esk13_2(X2992,X2993))
| c_SEQ_Omonoseq(X2993,X2992)
| ~ class_Orderings_Oorder(X2993) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2993,hAPP(X2992,esk13_2(X2992,X2993)),hAPP(X2992,esk12_2(X2992,X2993)))
| c_SEQ_Omonoseq(X2993,X2992)
| ~ class_Orderings_Oorder(X2993) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monoseq__def])])])])]) ).
cnf(i_0_1783,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_1336]) ).
fof(i_0_1784,plain,
! [X5374,X5375] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5375)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5374)
| c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X5375,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5374))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X5375),X5374) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__div__nat])]) ).
cnf(i_0_1785,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_1337]) ).
fof(i_0_1786,plain,
! [X5074,X5075,X5076,X5077] :
( ~ class_Groups_Omonoid__mult(X5077)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5077),X5076),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5075),X5074)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5077),hAPP(hAPP(c_Power_Opower__class_Opower(X5077),X5076),X5075)),X5074) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_1787,plain,
! [X4983,X4984,X4985,X4986] :
( ~ class_Rings_Ocomm__semiring__1(X4986)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4986),hAPP(hAPP(c_Power_Opower__class_Opower(X4986),X4985),X4984)),X4983) = hAPP(hAPP(c_Power_Opower__class_Opower(X4986),X4985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4984),X4983)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).
fof(i_0_1788,plain,
! [X4531,X4532,X4533] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4533,X4532)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4531)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4531),X4533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4531),X4532)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_1789,plain,
! [X4783,X4784,X4785] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4785)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4784,X4783)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4785),X4784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4785),X4783)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2])]) ).
fof(i_0_1790,plain,
! [X4777,X4778,X4779] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4779,X4778)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4777)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4779),X4777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4778),X4777)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_1791,plain,
! [X4780,X4781,X4782] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4782,X4781)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4780)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4780),X4782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4780),X4781)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_1792,plain,
! [X5052,X5053] :
( ( X5053 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5052),X5053) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X5053 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5052),X5053) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5052),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5052),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5053,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_1793,plain,
! [X3237,X3238,X3239] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3239,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3238,X3237))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3239,X3237),X3238) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3239,X3237),X3238)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3239,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3238,X3237)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).
fof(i_0_1794,plain,
! [X3589,X3590,X3591] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3591,X3590),X3589)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3591,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3589,X3590)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3591,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3589,X3590))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3591,X3590),X3589) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).
cnf(i_0_1795,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1338]) ).
fof(i_0_1796,plain,
! [X4733,X4734,X4735,X4736] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4736,X4735)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4734,X4733)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4736),X4734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4735),X4733)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).
fof(i_0_1797,plain,
! [X3567,X3568,X3569] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3569,X3568)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3568,X3569),X3567) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3568,X3567),X3569) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).
fof(i_0_1798,plain,
! [X3564,X3565,X3566] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3566,X3565)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3565,X3564),X3566) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3565,X3566),X3564) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).
fof(i_0_1799,plain,
! [X3570,X3571,X3572] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3572,X3571)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3570,X3571),X3572) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3570,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3571,X3572)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).
fof(i_0_1800,plain,
! [X3592,X3593,X3594] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3594,X3593)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3592,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3593,X3594)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3592,X3594),X3593) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).
fof(i_0_1801,plain,
! [X3581,X3582,X3583] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3583,X3582)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3581,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3582,X3583)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3581,X3582),X3583) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).
fof(i_0_1802,plain,
! [X5233,X5234] :
( ( ~ 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,X5233,X5234))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5233)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5234) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5233)
| 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,X5233,X5234))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5234) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).
fof(i_0_1803,plain,
! [X5286,X5287] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5286,X5287),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5286)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5287,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5286)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5286,X5287),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5287,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff])])]) ).
fof(i_0_1804,plain,
! [X5284,X5285] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5284,X5285),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5284,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5285) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5284,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5284,X5285),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5285) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])]) ).
fof(i_0_1805,plain,
! [X5220,X5221] :
( ( ~ 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,X5220,X5221))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5220,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5221,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5220,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,X5220,X5221))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5221,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_1806,plain,
! [X5231,X5232] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5231,X5232))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5232,X5231)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5232) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5232,X5231)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5231,X5232))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5232) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).
fof(i_0_1807,plain,
! [X5239,X5240,X5241] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5241)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5240,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5239),X5241)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5240,X5239),X5241) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])]) ).
fof(i_0_1808,plain,
! [X4317,X4318,X4319] :
( ( c_Orderings_Oord__class_Oless__eq(X4319,X4318,c_Groups_Ozero__class_Ozero(X4319))
| c_Orderings_Oord__class_Oless__eq(X4319,c_Groups_Ozero__class_Ozero(X4319),X4318)
| ~ c_Orderings_Oord__class_Oless__eq(X4319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4319),X4318),X4317),c_Groups_Ozero__class_Ozero(X4319))
| ~ class_Rings_Olinordered__ring__strict(X4319) )
& ( c_Orderings_Oord__class_Oless__eq(X4319,c_Groups_Ozero__class_Ozero(X4319),X4317)
| c_Orderings_Oord__class_Oless__eq(X4319,c_Groups_Ozero__class_Ozero(X4319),X4318)
| ~ c_Orderings_Oord__class_Oless__eq(X4319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4319),X4318),X4317),c_Groups_Ozero__class_Ozero(X4319))
| ~ class_Rings_Olinordered__ring__strict(X4319) )
& ( c_Orderings_Oord__class_Oless__eq(X4319,X4318,c_Groups_Ozero__class_Ozero(X4319))
| c_Orderings_Oord__class_Oless__eq(X4319,X4317,c_Groups_Ozero__class_Ozero(X4319))
| ~ c_Orderings_Oord__class_Oless__eq(X4319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4319),X4318),X4317),c_Groups_Ozero__class_Ozero(X4319))
| ~ class_Rings_Olinordered__ring__strict(X4319) )
& ( c_Orderings_Oord__class_Oless__eq(X4319,c_Groups_Ozero__class_Ozero(X4319),X4317)
| c_Orderings_Oord__class_Oless__eq(X4319,X4317,c_Groups_Ozero__class_Ozero(X4319))
| ~ c_Orderings_Oord__class_Oless__eq(X4319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4319),X4318),X4317),c_Groups_Ozero__class_Ozero(X4319))
| ~ class_Rings_Olinordered__ring__strict(X4319) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4319,c_Groups_Ozero__class_Ozero(X4319),X4318)
| ~ c_Orderings_Oord__class_Oless__eq(X4319,X4317,c_Groups_Ozero__class_Ozero(X4319))
| c_Orderings_Oord__class_Oless__eq(X4319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4319),X4318),X4317),c_Groups_Ozero__class_Ozero(X4319))
| ~ class_Rings_Olinordered__ring__strict(X4319) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4319,X4318,c_Groups_Ozero__class_Ozero(X4319))
| ~ c_Orderings_Oord__class_Oless__eq(X4319,c_Groups_Ozero__class_Ozero(X4319),X4317)
| c_Orderings_Oord__class_Oless__eq(X4319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4319),X4318),X4317),c_Groups_Ozero__class_Ozero(X4319))
| ~ class_Rings_Olinordered__ring__strict(X4319) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
fof(i_0_1809,plain,
! [X4314,X4315,X4316] :
( ( c_Orderings_Oord__class_Oless__eq(X4316,X4315,c_Groups_Ozero__class_Ozero(X4316))
| c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),X4315)
| ~ c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4316),X4315),X4314))
| ~ class_Rings_Olinordered__ring__strict(X4316) )
& ( c_Orderings_Oord__class_Oless__eq(X4316,X4314,c_Groups_Ozero__class_Ozero(X4316))
| c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),X4315)
| ~ c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4316),X4315),X4314))
| ~ class_Rings_Olinordered__ring__strict(X4316) )
& ( c_Orderings_Oord__class_Oless__eq(X4316,X4315,c_Groups_Ozero__class_Ozero(X4316))
| c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),X4314)
| ~ c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4316),X4315),X4314))
| ~ class_Rings_Olinordered__ring__strict(X4316) )
& ( c_Orderings_Oord__class_Oless__eq(X4316,X4314,c_Groups_Ozero__class_Ozero(X4316))
| c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),X4314)
| ~ c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4316),X4315),X4314))
| ~ class_Rings_Olinordered__ring__strict(X4316) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),X4315)
| ~ c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),X4314)
| c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4316),X4315),X4314))
| ~ class_Rings_Olinordered__ring__strict(X4316) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4316,X4315,c_Groups_Ozero__class_Ozero(X4316))
| ~ c_Orderings_Oord__class_Oless__eq(X4316,X4314,c_Groups_Ozero__class_Ozero(X4316))
| c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Ozero__class_Ozero(X4316),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4316),X4315),X4314))
| ~ class_Rings_Olinordered__ring__strict(X4316) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).
fof(i_0_1810,plain,
! [X5054,X5055] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X5055)),X5054))
| X5055 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X5054 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5055 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X5055)),X5054)) )
& ( X5054 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X5055)),X5054)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])]) ).
fof(i_0_1811,plain,
! [X4241,X4242,X4243] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4243),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4242,X4241)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4243),X4242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4243),X4241)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(i_0_1812,plain,
! [X4150,X4151,X4152] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4152),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4151,X4150)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4152),X4151),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4152),X4150)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_1813,plain,
! [X4751,X4752,X4753] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4753),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4752,X4751)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4753),X4752),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4753),X4751)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(i_0_1814,plain,
! [X4709,X4710,X4711] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4711),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4710,X4709)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4711),X4710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4711),X4709)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
fof(i_0_1815,plain,
! [X4508,X4509] :
( ~ class_Rings_Ocomm__semiring__1(X4509)
| c_Groups_Oplus__class_Oplus(X4509,X4508,X4508) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4509),c_Groups_Oplus__class_Oplus(X4509,c_Groups_Oone__class_Oone(X4509),c_Groups_Oone__class_Oone(X4509))),X4508) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).
fof(i_0_1816,plain,
! [X5326,X5327,X5328] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5328)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5328),X5327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5328),X5326)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5327,X5326) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])]) ).
fof(i_0_1817,plain,
! [X4803,X4804] :
( ( X4804 = 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),X4804),X4804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4803),X4803)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4803 = 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),X4804),X4804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4803),X4803)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4804 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X4803 != 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),X4804),X4804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4803),X4803)) = 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])])]) ).
fof(i_0_1818,plain,
! [X5044,X5045] :
( ( ~ 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),X5045),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X5044)))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X5044) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5045) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X5044) != 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),X5045),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X5044))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5045)
| 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),X5045),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X5044))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq__number__of])])]) ).
cnf(i_0_1819,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_1339]) ).
cnf(i_0_1820,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_1340]) ).
cnf(i_0_1821,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_1341]) ).
cnf(i_0_1822,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_1342]) ).
fof(i_0_1823,plain,
! [X3249,X3250,X3251] :
( ~ class_Groups_Oordered__comm__monoid__add(X3251)
| ~ c_Orderings_Oord__class_Oless(X3251,X3250,c_Groups_Ozero__class_Ozero(X3251))
| ~ c_Orderings_Oord__class_Oless(X3251,X3249,c_Groups_Ozero__class_Ozero(X3251))
| c_Orderings_Oord__class_Oless(X3251,c_Groups_Oplus__class_Oplus(X3251,X3250,X3249),c_Groups_Ozero__class_Ozero(X3251)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_1824,plain,
! [X3296,X3297,X3298] :
( ~ class_Groups_Oordered__comm__monoid__add(X3298)
| ~ c_Orderings_Oord__class_Oless__eq(X3298,X3297,c_Groups_Ozero__class_Ozero(X3298))
| ~ c_Orderings_Oord__class_Oless(X3298,X3296,c_Groups_Ozero__class_Ozero(X3298))
| c_Orderings_Oord__class_Oless(X3298,c_Groups_Oplus__class_Oplus(X3298,X3297,X3296),c_Groups_Ozero__class_Ozero(X3298)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_1825,plain,
! [X3293,X3294,X3295] :
( ~ class_Groups_Oordered__comm__monoid__add(X3295)
| ~ c_Orderings_Oord__class_Oless(X3295,X3294,c_Groups_Ozero__class_Ozero(X3295))
| ~ c_Orderings_Oord__class_Oless__eq(X3295,X3293,c_Groups_Ozero__class_Ozero(X3295))
| c_Orderings_Oord__class_Oless(X3295,c_Groups_Oplus__class_Oplus(X3295,X3294,X3293),c_Groups_Ozero__class_Ozero(X3295)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_1826,plain,
! [X3637,X3638,X3639] :
( ~ class_Groups_Oordered__comm__monoid__add(X3639)
| ~ c_Orderings_Oord__class_Oless__eq(X3639,X3638,c_Groups_Ozero__class_Ozero(X3639))
| ~ c_Orderings_Oord__class_Oless__eq(X3639,X3637,c_Groups_Ozero__class_Ozero(X3639))
| c_Orderings_Oord__class_Oless__eq(X3639,c_Groups_Oplus__class_Oplus(X3639,X3638,X3637),c_Groups_Ozero__class_Ozero(X3639)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_1827,plain,
! [X3246,X3247,X3248] :
( ~ class_Groups_Oordered__comm__monoid__add(X3248)
| ~ c_Orderings_Oord__class_Oless(X3248,c_Groups_Ozero__class_Ozero(X3248),X3247)
| ~ c_Orderings_Oord__class_Oless(X3248,c_Groups_Ozero__class_Ozero(X3248),X3246)
| c_Orderings_Oord__class_Oless(X3248,c_Groups_Ozero__class_Ozero(X3248),c_Groups_Oplus__class_Oplus(X3248,X3247,X3246)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_1828,plain,
! [X3282,X3283,X3284] :
( ~ class_Groups_Oordered__comm__monoid__add(X3284)
| ~ c_Orderings_Oord__class_Oless__eq(X3284,c_Groups_Ozero__class_Ozero(X3284),X3283)
| ~ c_Orderings_Oord__class_Oless(X3284,c_Groups_Ozero__class_Ozero(X3284),X3282)
| c_Orderings_Oord__class_Oless(X3284,c_Groups_Ozero__class_Ozero(X3284),c_Groups_Oplus__class_Oplus(X3284,X3283,X3282)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_1829,plain,
! [X3279,X3280,X3281] :
( ~ class_Groups_Oordered__comm__monoid__add(X3281)
| ~ c_Orderings_Oord__class_Oless(X3281,c_Groups_Ozero__class_Ozero(X3281),X3280)
| ~ c_Orderings_Oord__class_Oless__eq(X3281,c_Groups_Ozero__class_Ozero(X3281),X3279)
| c_Orderings_Oord__class_Oless(X3281,c_Groups_Ozero__class_Ozero(X3281),c_Groups_Oplus__class_Oplus(X3281,X3280,X3279)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_1830,plain,
! [X3623,X3624,X3625] :
( ~ class_Groups_Oordered__comm__monoid__add(X3625)
| ~ c_Orderings_Oord__class_Oless__eq(X3625,c_Groups_Ozero__class_Ozero(X3625),X3624)
| ~ c_Orderings_Oord__class_Oless__eq(X3625,c_Groups_Ozero__class_Ozero(X3625),X3623)
| c_Orderings_Oord__class_Oless__eq(X3625,c_Groups_Ozero__class_Ozero(X3625),c_Groups_Oplus__class_Oplus(X3625,X3624,X3623)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_1831,plain,
! [X3911,X3912] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3912),X3911)
| c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3911,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3912))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X3911),X3912) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__subtract])]) ).
fof(i_0_1832,plain,
! [X3793,X3794] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3794),X3793)
| c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3793,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3794))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X3793),X3794) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__subtract])]) ).
fof(i_0_1833,plain,
! [X3275,X3276] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3276,X3275))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3276)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3275) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3276)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3276,X3275)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3275)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3276,X3275)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_1834,plain,
! [X5041,X5042,X5043] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5043),X5042)),X5041) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5042),X5041)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_1835,plain,
! [X4233,X4234,X4235] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4235),X4234)),X4233) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4235),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4234),X4233)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_1836,plain,
! [X4717,X4718,X4719] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4719),X4718)),X4717) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4718),X4717)),
inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).
fof(i_0_1837,plain,
! [X4722,X4723,X4724] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4724),X4723)),X4722) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4723),X4722)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_1838,plain,
! [X4404,X4405,X4406] :
( ~ class_Rings_Olinordered__semiring__strict(X4406)
| ~ c_Orderings_Oord__class_Oless(X4406,X4405,c_Groups_Ozero__class_Ozero(X4406))
| ~ c_Orderings_Oord__class_Oless(X4406,c_Groups_Ozero__class_Ozero(X4406),X4404)
| c_Orderings_Oord__class_Oless(X4406,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4406),X4405),X4404),c_Groups_Ozero__class_Ozero(X4406)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_1839,plain,
! [X4388,X4389,X4390] :
( ~ class_Rings_Olinordered__semiring__strict(X4390)
| ~ c_Orderings_Oord__class_Oless(X4390,c_Groups_Ozero__class_Ozero(X4390),X4389)
| ~ c_Orderings_Oord__class_Oless(X4390,X4388,c_Groups_Ozero__class_Ozero(X4390))
| c_Orderings_Oord__class_Oless(X4390,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4390),X4389),X4388),c_Groups_Ozero__class_Ozero(X4390)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_1840,plain,
! [X4391,X4392,X4393] :
( ~ class_Rings_Olinordered__semiring__strict(X4393)
| ~ c_Orderings_Oord__class_Oless(X4393,c_Groups_Ozero__class_Ozero(X4393),X4392)
| ~ c_Orderings_Oord__class_Oless(X4393,X4391,c_Groups_Ozero__class_Ozero(X4393))
| c_Orderings_Oord__class_Oless(X4393,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4393),X4391),X4392),c_Groups_Ozero__class_Ozero(X4393)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_1841,plain,
! [X4368,X4369,X4370] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4370,c_Groups_Ozero__class_Ozero(X4370),X4369)
| ~ c_Orderings_Oord__class_Oless__eq(X4370,X4368,c_Groups_Ozero__class_Ozero(X4370))
| c_Orderings_Oord__class_Oless__eq(X4370,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4370),X4369),X4368),c_Groups_Ozero__class_Ozero(X4370))
| ~ class_Rings_Oordered__cancel__semiring(X4370) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4370,X4369,c_Groups_Ozero__class_Ozero(X4370))
| ~ c_Orderings_Oord__class_Oless__eq(X4370,c_Groups_Ozero__class_Ozero(X4370),X4368)
| c_Orderings_Oord__class_Oless__eq(X4370,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4370),X4369),X4368),c_Groups_Ozero__class_Ozero(X4370))
| ~ class_Rings_Oordered__cancel__semiring(X4370) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).
fof(i_0_1842,plain,
! [X4329,X4330,X4331] :
( ~ class_Rings_Oordered__cancel__semiring(X4331)
| ~ c_Orderings_Oord__class_Oless__eq(X4331,X4330,c_Groups_Ozero__class_Ozero(X4331))
| ~ c_Orderings_Oord__class_Oless__eq(X4331,c_Groups_Ozero__class_Ozero(X4331),X4329)
| c_Orderings_Oord__class_Oless__eq(X4331,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4331),X4330),X4329),c_Groups_Ozero__class_Ozero(X4331)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).
fof(i_0_1843,plain,
! [X4323,X4324,X4325] :
( ~ class_Rings_Oordered__cancel__semiring(X4325)
| ~ c_Orderings_Oord__class_Oless__eq(X4325,c_Groups_Ozero__class_Ozero(X4325),X4324)
| ~ c_Orderings_Oord__class_Oless__eq(X4325,X4323,c_Groups_Ozero__class_Ozero(X4325))
| c_Orderings_Oord__class_Oless__eq(X4325,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4325),X4324),X4323),c_Groups_Ozero__class_Ozero(X4325)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).
fof(i_0_1844,plain,
! [X4326,X4327,X4328] :
( ~ class_Rings_Oordered__cancel__semiring(X4328)
| ~ c_Orderings_Oord__class_Oless__eq(X4328,c_Groups_Ozero__class_Ozero(X4328),X4327)
| ~ c_Orderings_Oord__class_Oless__eq(X4328,X4326,c_Groups_Ozero__class_Ozero(X4328))
| c_Orderings_Oord__class_Oless__eq(X4328,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4328),X4326),X4327),c_Groups_Ozero__class_Ozero(X4328)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).
fof(i_0_1845,plain,
! [X4385,X4386,X4387] :
( ~ class_Rings_Olinordered__semiring__strict(X4387)
| ~ c_Orderings_Oord__class_Oless(X4387,c_Groups_Ozero__class_Ozero(X4387),X4386)
| ~ c_Orderings_Oord__class_Oless(X4387,c_Groups_Ozero__class_Ozero(X4387),X4385)
| c_Orderings_Oord__class_Oless(X4387,c_Groups_Ozero__class_Ozero(X4387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4387),X4386),X4385)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_1846,plain,
! [X4462,X4463,X4464] :
( ~ class_Rings_Olinordered__semidom(X4464)
| ~ c_Orderings_Oord__class_Oless(X4464,c_Groups_Oone__class_Oone(X4464),X4463)
| ~ c_Orderings_Oord__class_Oless(X4464,c_Groups_Oone__class_Oone(X4464),X4462)
| c_Orderings_Oord__class_Oless(X4464,c_Groups_Oone__class_Oone(X4464),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4464),X4463),X4462)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_1847,plain,
! [X4365,X4366,X4367] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4367,c_Groups_Ozero__class_Ozero(X4367),X4366)
| ~ c_Orderings_Oord__class_Oless__eq(X4367,c_Groups_Ozero__class_Ozero(X4367),X4365)
| c_Orderings_Oord__class_Oless__eq(X4367,c_Groups_Ozero__class_Ozero(X4367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4367),X4366),X4365))
| ~ class_Rings_Oordered__ring(X4367) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4367,X4366,c_Groups_Ozero__class_Ozero(X4367))
| ~ c_Orderings_Oord__class_Oless__eq(X4367,X4365,c_Groups_Ozero__class_Ozero(X4367))
| c_Orderings_Oord__class_Oless__eq(X4367,c_Groups_Ozero__class_Ozero(X4367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4367),X4366),X4365))
| ~ class_Rings_Oordered__ring(X4367) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).
fof(i_0_1848,plain,
! [X4320,X4321,X4322] :
( ~ class_Rings_Oordered__cancel__semiring(X4322)
| ~ c_Orderings_Oord__class_Oless__eq(X4322,c_Groups_Ozero__class_Ozero(X4322),X4321)
| ~ c_Orderings_Oord__class_Oless__eq(X4322,c_Groups_Ozero__class_Ozero(X4322),X4320)
| c_Orderings_Oord__class_Oless__eq(X4322,c_Groups_Ozero__class_Ozero(X4322),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4322),X4321),X4320)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).
fof(i_0_1849,plain,
! [X4407,X4408,X4409] :
( ~ class_Rings_Olinordered__ring__strict(X4409)
| ~ c_Orderings_Oord__class_Oless(X4409,X4408,c_Groups_Ozero__class_Ozero(X4409))
| ~ c_Orderings_Oord__class_Oless(X4409,X4407,c_Groups_Ozero__class_Ozero(X4409))
| c_Orderings_Oord__class_Oless(X4409,c_Groups_Ozero__class_Ozero(X4409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4409),X4408),X4407)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_1850,plain,
! [X4332,X4333,X4334] :
( ~ class_Rings_Oordered__ring(X4334)
| ~ c_Orderings_Oord__class_Oless__eq(X4334,X4333,c_Groups_Ozero__class_Ozero(X4334))
| ~ c_Orderings_Oord__class_Oless__eq(X4334,X4332,c_Groups_Ozero__class_Ozero(X4334))
| c_Orderings_Oord__class_Oless__eq(X4334,c_Groups_Ozero__class_Ozero(X4334),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4334),X4333),X4332)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).
fof(i_0_1851,plain,
! [X3385,X3386,X3387,X3388] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3388)
| ~ c_Orderings_Oord__class_Oless(X3388,X3387,X3386)
| c_Orderings_Oord__class_Oless(X3388,c_Groups_Oplus__class_Oplus(X3388,X3387,X3385),c_Groups_Oplus__class_Oplus(X3388,X3386,X3385)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_1852,plain,
! [X3389,X3390,X3391,X3392] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3392)
| ~ c_Orderings_Oord__class_Oless(X3392,X3391,X3390)
| c_Orderings_Oord__class_Oless(X3392,c_Groups_Oplus__class_Oplus(X3392,X3389,X3391),c_Groups_Oplus__class_Oplus(X3392,X3389,X3390)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_1853,plain,
! [X2760,X2761,X2762,X2763] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2763)
| ~ c_Orderings_Oord__class_Oless__eq(X2763,X2762,X2761)
| c_Orderings_Oord__class_Oless__eq(X2763,c_Groups_Oplus__class_Oplus(X2763,X2762,X2760),c_Groups_Oplus__class_Oplus(X2763,X2761,X2760)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_1854,plain,
! [X2764,X2765,X2766,X2767] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2767)
| ~ c_Orderings_Oord__class_Oless__eq(X2767,X2766,X2765)
| c_Orderings_Oord__class_Oless__eq(X2767,c_Groups_Oplus__class_Oplus(X2767,X2764,X2766),c_Groups_Oplus__class_Oplus(X2767,X2764,X2765)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_1855,plain,
! [X3918,X3919] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X3919),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3918)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3919,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3918)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt])]) ).
cnf(i_0_1856,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_1326]) ).
cnf(i_0_1857,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_1343]) ).
cnf(i_0_1858,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_1327]) ).
fof(i_0_1859,plain,
! [X5302,X5303,X5305] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk72_2(X5302,X5303))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5302)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5303) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk72_2(X5302,X5303)),X5303) = X5302
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5302)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5303) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5305)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5305),X5303) != X5302
| X5305 = esk72_2(X5302,X5303)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5302)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5303) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth__unique])])])])]) ).
fof(i_0_1860,plain,
! [X5182,X5183,X5184] :
( ~ class_Rings_Olinordered__semidom(X5184)
| ~ c_Orderings_Oord__class_Oless(X5184,c_Groups_Oone__class_Oone(X5184),X5183)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5182)
| c_Orderings_Oord__class_Oless(X5184,c_Groups_Oone__class_Oone(X5184),hAPP(hAPP(c_Power_Opower__class_Opower(X5184),X5183),X5182)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
fof(i_0_1861,plain,
! [X3050,X3051] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk19_2(X3050,X3051),esk20_2(X3050,X3051))
| c_SEQ_Omonoseq(X3051,X3050)
| ~ class_Orderings_Oorder(X3051) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3051,hAPP(X3050,esk19_2(X3050,X3051)),hAPP(X3050,esk20_2(X3050,X3051)))
| c_SEQ_Omonoseq(X3051,X3050)
| ~ class_Orderings_Oorder(X3051) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monoI1])])])]) ).
fof(i_0_1862,plain,
! [X3046,X3047] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk17_2(X3046,X3047),esk18_2(X3046,X3047))
| c_SEQ_Omonoseq(X3047,X3046)
| ~ class_Orderings_Oorder(X3047) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3047,hAPP(X3046,esk18_2(X3046,X3047)),hAPP(X3046,esk17_2(X3046,X3047)))
| c_SEQ_Omonoseq(X3047,X3046)
| ~ class_Orderings_Oorder(X3047) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monoI2])])])]) ).
fof(i_0_1863,plain,
! [X2986,X2987,X2988,X2989] :
( ( ~ c_SEQ_Oincseq(X2987,X2986)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2988,X2989)
| c_Orderings_Oord__class_Oless__eq(X2987,hAPP(X2986,X2988),hAPP(X2986,X2989))
| ~ class_Orderings_Oorder(X2987) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk8_2(X2986,X2987),esk9_2(X2986,X2987))
| c_SEQ_Oincseq(X2987,X2986)
| ~ class_Orderings_Oorder(X2987) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2987,hAPP(X2986,esk8_2(X2986,X2987)),hAPP(X2986,esk9_2(X2986,X2987)))
| c_SEQ_Oincseq(X2987,X2986)
| ~ class_Orderings_Oorder(X2987) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incseq__def])])])])]) ).
fof(i_0_1864,plain,
! [X2980,X2981,X2982,X2983] :
( ( ~ c_SEQ_Odecseq(X2981,X2980)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2982,X2983)
| c_Orderings_Oord__class_Oless__eq(X2981,hAPP(X2980,X2983),hAPP(X2980,X2982))
| ~ class_Orderings_Oorder(X2981) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk6_2(X2980,X2981),esk7_2(X2980,X2981))
| c_SEQ_Odecseq(X2981,X2980)
| ~ class_Orderings_Oorder(X2981) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2981,hAPP(X2980,esk7_2(X2980,X2981)),hAPP(X2980,esk6_2(X2980,X2981)))
| c_SEQ_Odecseq(X2981,X2980)
| ~ class_Orderings_Oorder(X2981) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decseq__def])])])])]) ).
fof(i_0_1865,plain,
! [X3982,X3983] :
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3983))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3982)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3982,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X3983))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X3982),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3983)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1344])]) ).
fof(i_0_1866,plain,
! [X3980,X3981] :
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3981))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3980)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3980,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X3981))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X3980),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3981)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1345])]) ).
fof(i_0_1867,plain,
! [X3661,X3662,X3663,X3664] :
( ~ class_Rings_Olinordered__semidom(X3664)
| ~ c_Orderings_Oord__class_Oless(X3664,c_Groups_Ozero__class_Ozero(X3664),X3663)
| ~ c_Orderings_Oord__class_Oless(X3664,X3662,X3661)
| c_Orderings_Oord__class_Oless(X3664,X3662,c_Groups_Oplus__class_Oplus(X3664,X3663,X3661)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_1868,plain,
! [X3289,X3290,X3291,X3292] :
( ~ class_Groups_Oordered__comm__monoid__add(X3292)
| ~ c_Orderings_Oord__class_Oless__eq(X3292,c_Groups_Ozero__class_Ozero(X3292),X3291)
| ~ c_Orderings_Oord__class_Oless(X3292,X3290,X3289)
| c_Orderings_Oord__class_Oless(X3292,X3290,c_Groups_Oplus__class_Oplus(X3292,X3291,X3289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_1869,plain,
! [X3285,X3286,X3287,X3288] :
( ~ class_Groups_Oordered__comm__monoid__add(X3288)
| ~ c_Orderings_Oord__class_Oless(X3288,c_Groups_Ozero__class_Ozero(X3288),X3287)
| ~ c_Orderings_Oord__class_Oless__eq(X3288,X3286,X3285)
| c_Orderings_Oord__class_Oless(X3288,X3286,c_Groups_Oplus__class_Oplus(X3288,X3287,X3285)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_1870,plain,
! [X3629,X3630,X3631,X3632] :
( ~ class_Groups_Oordered__comm__monoid__add(X3632)
| ~ c_Orderings_Oord__class_Oless__eq(X3632,c_Groups_Ozero__class_Ozero(X3632),X3631)
| ~ c_Orderings_Oord__class_Oless__eq(X3632,X3630,X3629)
| c_Orderings_Oord__class_Oless__eq(X3632,X3630,c_Groups_Oplus__class_Oplus(X3632,X3631,X3629)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_1871,plain,
! [X3633,X3634,X3635,X3636] :
( ~ class_Groups_Oordered__comm__monoid__add(X3636)
| ~ c_Orderings_Oord__class_Oless__eq(X3636,c_Groups_Ozero__class_Ozero(X3636),X3635)
| ~ c_Orderings_Oord__class_Oless__eq(X3636,X3634,X3633)
| c_Orderings_Oord__class_Oless__eq(X3636,X3634,c_Groups_Oplus__class_Oplus(X3636,X3633,X3635)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_1872,plain,
! [X3782,X3783,X3784] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3784,c_Int_Onumber__class_Onumber__of(X3784,X3783),c_Int_Onumber__class_Onumber__of(X3784,X3782))
| ~ c_Orderings_Oord__class_Oless(X3784,c_Int_Onumber__class_Onumber__of(X3784,X3782),c_Int_Onumber__class_Onumber__of(X3784,X3783))
| ~ class_Int_Onumber(X3784)
| ~ class_Orderings_Olinorder(X3784) )
& ( c_Orderings_Oord__class_Oless(X3784,c_Int_Onumber__class_Onumber__of(X3784,X3782),c_Int_Onumber__class_Onumber__of(X3784,X3783))
| c_Orderings_Oord__class_Oless__eq(X3784,c_Int_Onumber__class_Onumber__of(X3784,X3783),c_Int_Onumber__class_Onumber__of(X3784,X3782))
| ~ class_Int_Onumber(X3784)
| ~ class_Orderings_Olinorder(X3784) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1346])])]) ).
cnf(i_0_1873,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(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),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1347]) ).
fof(i_0_1874,plain,
! [X4540,X4541,X4542] :
( ~ class_Rings_Oring__1(X4542)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4541,X4540)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4542),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4540,X4541)) = c_Groups_Ominus__class_Ominus(X4542,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4542),X4540),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4542),X4541)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__diff])]) ).
cnf(i_0_1875,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),X2) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_1348]) ).
fof(i_0_1876,plain,
! [X3845,X3846,X3847] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3847,X3846)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3847,X3845),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3846,X3845)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_1877,plain,
! [X3489,X3490,X3491] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3491,X3490)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3491,X3489),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3490,X3489)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_1878,plain,
! [X3862,X3863,X3864] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3864,X3863)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3862,X3864),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3862,X3863)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).
fof(i_0_1879,plain,
! [X2969,X2970,X2971] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2971,X2970)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2969,X2971),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2969,X2970)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).
fof(i_0_1880,plain,
! [X5317,X5318,X5319] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5319,X5318)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5319,X5317),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5318,X5317)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])]) ).
fof(i_0_1881,plain,
! [X3435,X3436,X3437] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3437,X3436)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3437,X3435),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3436,X3435)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).
fof(i_0_1882,plain,
! [X3438,X3439,X3440] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3440,X3439)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3438,X3439),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3438,X3440)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).
fof(i_0_1883,plain,
! [X2817,X2818,X2819] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2819,X2818)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2819,X2817),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2818,X2817)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
cnf(i_0_1884,plain,
( X1 = c_Nat_OSuc(esk24_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_1349]) ).
cnf(i_0_1885,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_1350]) ).
fof(i_0_1886,plain,
! [X5253,X5254,X5255] :
( ~ class_Divides_Osemiring__div(X5255)
| X5254 = c_Groups_Ozero__class_Ozero(X5255)
| c_Divides_Odiv__class_Odiv(X5255,c_Groups_Oplus__class_Oplus(X5255,X5254,X5253),X5254) = c_Groups_Oplus__class_Oplus(X5255,c_Divides_Odiv__class_Odiv(X5255,X5253,X5254),c_Groups_Oone__class_Oone(X5255)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).
fof(i_0_1887,plain,
! [X5250,X5251,X5252] :
( ~ class_Divides_Osemiring__div(X5252)
| X5251 = c_Groups_Ozero__class_Ozero(X5252)
| c_Divides_Odiv__class_Odiv(X5252,c_Groups_Oplus__class_Oplus(X5252,X5250,X5251),X5251) = c_Groups_Oplus__class_Oplus(X5252,c_Divides_Odiv__class_Odiv(X5252,X5250,X5251),c_Groups_Oone__class_Oone(X5252)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).
cnf(i_0_1888,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_1351]) ).
cnf(i_0_1889,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_1352]) ).
cnf(i_0_1890,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk24_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_1349]) ).
fof(i_0_1891,plain,
! [X3721,X3722,X3723] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3723)
| c_Groups_Oabs__class_Oabs(X3723,c_Groups_Oplus__class_Oplus(X3723,c_Groups_Oabs__class_Oabs(X3723,X3722),c_Groups_Oabs__class_Oabs(X3723,X3721))) = c_Groups_Oplus__class_Oplus(X3723,c_Groups_Oabs__class_Oabs(X3723,X3722),c_Groups_Oabs__class_Oabs(X3723,X3721)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).
fof(i_0_1892,plain,
! [X5288,X5289] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5289,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5288)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5289,X5288),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0])]) ).
fof(i_0_1893,plain,
! [X5224,X5225] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5225)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5224,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,X5225,X5224),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_1894,plain,
! [X5218,X5219] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5219,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5218)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5219,X5218),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_1895,plain,
! [X5282,X5283] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5283)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5282)
| 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,X5283,X5282)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_1896,plain,
! [X3971,X3972] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3972)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3971)
| 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,X3972,X3971)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
cnf(i_0_1897,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_1353]) ).
cnf(i_0_1898,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_1349]) ).
fof(i_0_1899,plain,
! [X3430,X3431,X3432] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3431,X3432) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3430,X3432)
| X3431 = X3430
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3432,X3430)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3432,X3431) )
& ( X3431 != X3430
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3431,X3432) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3430,X3432)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3432,X3430)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3432,X3431) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).
fof(i_0_1900,plain,
! [X5237,X5238] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5238)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5237)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5238,X5237),X5238) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).
fof(i_0_1901,plain,
! [X5324,X5325] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5325)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5324)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5324,X5325),X5324) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])]) ).
fof(i_0_1902,plain,
! [X3149,X3150] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3150)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3149)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3149,X3150),X3149) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).
cnf(i_0_1903,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,c_Nat_OSuc(X2)))
| ~ c_SEQ_Osubseq(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1314]) ).
fof(i_0_1904,plain,
! [X3242,X3243] :
( ( ~ c_Orderings_Oord__class_Oless(X3243,c_Groups_Ozero__class_Ozero(X3243),c_Groups_Oplus__class_Oplus(X3243,X3242,X3242))
| c_Orderings_Oord__class_Oless(X3243,c_Groups_Ozero__class_Ozero(X3243),X3242)
| ~ class_Groups_Olinordered__ab__group__add(X3243) )
& ( ~ c_Orderings_Oord__class_Oless(X3243,c_Groups_Ozero__class_Ozero(X3243),X3242)
| c_Orderings_Oord__class_Oless(X3243,c_Groups_Ozero__class_Ozero(X3243),c_Groups_Oplus__class_Oplus(X3243,X3242,X3242))
| ~ class_Groups_Olinordered__ab__group__add(X3243) ) ),
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_1905,plain,
! [X3619,X3620] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3620,c_Groups_Ozero__class_Ozero(X3620),c_Groups_Oplus__class_Oplus(X3620,X3619,X3619))
| c_Orderings_Oord__class_Oless__eq(X3620,c_Groups_Ozero__class_Ozero(X3620),X3619)
| ~ class_Groups_Olinordered__ab__group__add(X3620) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3620,c_Groups_Ozero__class_Ozero(X3620),X3619)
| c_Orderings_Oord__class_Oless__eq(X3620,c_Groups_Ozero__class_Ozero(X3620),c_Groups_Oplus__class_Oplus(X3620,X3619,X3619))
| ~ class_Groups_Olinordered__ab__group__add(X3620) ) ),
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_1906,plain,
! [X3665,X3666] :
( ( ~ c_Orderings_Oord__class_Oless(X3666,c_Groups_Oplus__class_Oplus(X3666,X3665,X3665),c_Groups_Ozero__class_Ozero(X3666))
| c_Orderings_Oord__class_Oless(X3666,X3665,c_Groups_Ozero__class_Ozero(X3666))
| ~ class_Rings_Olinordered__idom(X3666) )
& ( ~ c_Orderings_Oord__class_Oless(X3666,X3665,c_Groups_Ozero__class_Ozero(X3666))
| c_Orderings_Oord__class_Oless(X3666,c_Groups_Oplus__class_Oplus(X3666,X3665,X3665),c_Groups_Ozero__class_Ozero(X3666))
| ~ class_Rings_Olinordered__idom(X3666) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_1907,plain,
! [X3244,X3245] :
( ( ~ c_Orderings_Oord__class_Oless(X3245,c_Groups_Oplus__class_Oplus(X3245,X3244,X3244),c_Groups_Ozero__class_Ozero(X3245))
| c_Orderings_Oord__class_Oless(X3245,X3244,c_Groups_Ozero__class_Ozero(X3245))
| ~ class_Groups_Olinordered__ab__group__add(X3245) )
& ( ~ c_Orderings_Oord__class_Oless(X3245,X3244,c_Groups_Ozero__class_Ozero(X3245))
| c_Orderings_Oord__class_Oless(X3245,c_Groups_Oplus__class_Oplus(X3245,X3244,X3244),c_Groups_Ozero__class_Ozero(X3245))
| ~ class_Groups_Olinordered__ab__group__add(X3245) ) ),
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_1908,plain,
! [X3621,X3622] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3622,c_Groups_Oplus__class_Oplus(X3622,X3621,X3621),c_Groups_Ozero__class_Ozero(X3622))
| c_Orderings_Oord__class_Oless__eq(X3622,X3621,c_Groups_Ozero__class_Ozero(X3622))
| ~ class_Groups_Olinordered__ab__group__add(X3622) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3622,X3621,c_Groups_Ozero__class_Ozero(X3622))
| c_Orderings_Oord__class_Oless__eq(X3622,c_Groups_Oplus__class_Oplus(X3622,X3621,X3621),c_Groups_Ozero__class_Ozero(X3622))
| ~ class_Groups_Olinordered__ab__group__add(X3622) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])]) ).
fof(i_0_1909,plain,
! [X5367,X5368,X5369,X5370] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X5370,X5369)),c_Complex_Orcis(X5368,X5367)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5370),X5368),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5369,X5367)),
inference(variable_rename,[status(thm)],[fact_rcis__mult]) ).
cnf(i_0_1910,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_1354]) ).
fof(i_0_1911,plain,
! [X3024,X3025,X3026,X3027] :
( ~ class_Rings_Ocomm__semiring__1(X3027)
| c_Groups_Oplus__class_Oplus(X3027,c_Groups_Oplus__class_Oplus(X3027,X3026,X3025),X3024) = c_Groups_Oplus__class_Oplus(X3027,c_Groups_Oplus__class_Oplus(X3027,X3026,X3024),X3025) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_1912,plain,
! [X3020,X3021,X3022,X3023] :
( ~ class_Rings_Ocomm__semiring__1(X3023)
| c_Groups_Oplus__class_Oplus(X3023,c_Groups_Oplus__class_Oplus(X3023,X3022,X3021),X3020) = c_Groups_Oplus__class_Oplus(X3023,X3022,c_Groups_Oplus__class_Oplus(X3023,X3021,X3020)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_1913,plain,
! [X2920,X2921,X2922,X2923] :
( ~ class_Groups_Oab__semigroup__add(X2923)
| c_Groups_Oplus__class_Oplus(X2923,c_Groups_Oplus__class_Oplus(X2923,X2922,X2921),X2920) = c_Groups_Oplus__class_Oplus(X2923,X2922,c_Groups_Oplus__class_Oplus(X2923,X2921,X2920)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_1914,plain,
! [X3016,X3017,X3018,X3019] :
( ~ class_Rings_Ocomm__semiring__1(X3019)
| c_Groups_Oplus__class_Oplus(X3019,X3018,c_Groups_Oplus__class_Oplus(X3019,X3017,X3016)) = c_Groups_Oplus__class_Oplus(X3019,c_Groups_Oplus__class_Oplus(X3019,X3018,X3017),X3016) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_1915,plain,
! [X3012,X3013,X3014,X3015] :
( ~ class_Rings_Ocomm__semiring__1(X3015)
| c_Groups_Oplus__class_Oplus(X3015,X3014,c_Groups_Oplus__class_Oplus(X3015,X3013,X3012)) = c_Groups_Oplus__class_Oplus(X3015,X3013,c_Groups_Oplus__class_Oplus(X3015,X3014,X3012)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_1916,plain,
! [X3803] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3803),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X3803),
inference(variable_rename,[status(thm)],[i_0_1355]) ).
fof(i_0_1917,plain,
! [X5270,X5271,X5272,X5273] :
( ( X5272 != c_Groups_Ozero__class_Ozero(X5273)
| c_Divides_Odiv__class_Odiv(X5273,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5273),X5272),X5271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5273),X5272),X5270)) = c_Groups_Ozero__class_Ozero(X5273)
| ~ class_Divides_Osemiring__div(X5273) )
& ( X5272 = c_Groups_Ozero__class_Ozero(X5273)
| c_Divides_Odiv__class_Odiv(X5273,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5273),X5272),X5271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5273),X5272),X5270)) = c_Divides_Odiv__class_Odiv(X5273,X5271,X5270)
| ~ class_Divides_Osemiring__div(X5273) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if])])]) ).
fof(i_0_1918,plain,
! [X5256,X5257,X5258,X5259] :
( ~ class_Divides_Osemiring__div(X5259)
| X5258 = c_Groups_Ozero__class_Ozero(X5259)
| c_Divides_Odiv__class_Odiv(X5259,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5259),X5258),X5257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5259),X5258),X5256)) = c_Divides_Odiv__class_Odiv(X5259,X5257,X5256) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])]) ).
fof(i_0_1919,plain,
! [X5260,X5261,X5262,X5263] :
( ~ class_Divides_Osemiring__div(X5263)
| X5262 = c_Groups_Ozero__class_Ozero(X5263)
| c_Divides_Odiv__class_Odiv(X5263,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5263),X5261),X5262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5263),X5260),X5262)) = c_Divides_Odiv__class_Odiv(X5263,X5261,X5260) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult2])]) ).
fof(i_0_1920,plain,
! [X3123,X3124,X3125] :
( ( ~ c_Orderings_Oord__class_Oless(X3125,X3124,X3123)
| c_Orderings_Oord__class_Oless(X3125,c_Groups_Ominus__class_Ominus(X3125,X3124,X3123),c_Groups_Ozero__class_Ozero(X3125))
| ~ class_Groups_Oordered__ab__group__add(X3125) )
& ( ~ c_Orderings_Oord__class_Oless(X3125,c_Groups_Ominus__class_Ominus(X3125,X3124,X3123),c_Groups_Ozero__class_Ozero(X3125))
| c_Orderings_Oord__class_Oless(X3125,X3124,X3123)
| ~ class_Groups_Oordered__ab__group__add(X3125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).
fof(i_0_1921,plain,
! [X3254,X3255,X3256] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3256,X3255,X3254)
| c_Orderings_Oord__class_Oless__eq(X3256,c_Groups_Ominus__class_Ominus(X3256,X3255,X3254),c_Groups_Ozero__class_Ozero(X3256))
| ~ class_Groups_Oordered__ab__group__add(X3256) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3256,c_Groups_Ominus__class_Ominus(X3256,X3255,X3254),c_Groups_Ozero__class_Ozero(X3256))
| c_Orderings_Oord__class_Oless__eq(X3256,X3255,X3254)
| ~ class_Groups_Oordered__ab__group__add(X3256) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).
cnf(i_0_1922,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_1356]) ).
cnf(i_0_1923,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_1357]) ).
cnf(i_0_1924,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_1358]) ).
fof(i_0_1925,plain,
! [X4786,X4787] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4787)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4786)
| 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),X4787),X4786)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])]) ).
fof(i_0_1926,plain,
! [X4769,X4770] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4770)
| ~ 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),X4770),X4769)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4769)
| ~ 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),X4770),X4769)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4770)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4769)
| 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),X4770),X4769)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).
fof(i_0_1927,plain,
! [X4529,X4530] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4530)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4529)
| 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),X4530),X4529)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
cnf(i_0_1928,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_1359]) ).
cnf(i_0_1929,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_1360]) ).
cnf(i_0_1930,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_1361]) ).
fof(i_0_1931,plain,
! [X4650,X4651,X4652] :
( ~ class_Rings_Olinordered__idom(X4652)
| ~ c_Orderings_Oord__class_Oless__eq(X4652,c_Groups_Ozero__class_Ozero(X4652),X4651)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4652),c_Groups_Oabs__class_Oabs(X4652,X4650)),X4651) = c_Groups_Oabs__class_Oabs(X4652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4652),X4650),X4651)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).
fof(i_0_1932,plain,
! [X4743] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4743,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4743),X4743))),
inference(variable_rename,[status(thm)],[fact_le__cube]) ).
cnf(i_0_1933,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_1362]) ).
cnf(i_0_1934,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_1363]) ).
fof(i_0_1935,plain,
! [X3993,X3994] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3994),c_RComplete_Onatfloor(X3993))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X3994),X3993)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3993)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3994)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X3994),X3993)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3994),c_RComplete_Onatfloor(X3993))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3993)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3994)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1364])])]) ).
fof(i_0_1936,plain,
! [X3995,X3996] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3995),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3996))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3995,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X3996))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3995)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3996)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3995,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X3996))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3995),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3996))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3995)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3996)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1365])])]) ).
fof(i_0_1937,plain,
! [X4653,X4654] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4654,X4653)
| c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4653),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4654)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4653,X4654)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int])]) ).
fof(i_0_1938,plain,
! [X3676,X3677] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3677,X3676)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3676,X3677)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3676),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3677)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__diff])]) ).
fof(i_0_1939,plain,
! [X3219,X3220,X3221,X3222,X3223] :
( ( ~ c_Orderings_Oord__class_Oless(X3223,X3222,X3221)
| c_Orderings_Oord__class_Oless(X3223,X3220,X3219)
| c_Groups_Ominus__class_Ominus(X3223,X3222,X3221) != c_Groups_Ominus__class_Ominus(X3223,X3220,X3219)
| ~ class_Groups_Oordered__ab__group__add(X3223) )
& ( ~ c_Orderings_Oord__class_Oless(X3223,X3220,X3219)
| c_Orderings_Oord__class_Oless(X3223,X3222,X3221)
| c_Groups_Ominus__class_Ominus(X3223,X3222,X3221) != c_Groups_Ominus__class_Ominus(X3223,X3220,X3219)
| ~ class_Groups_Oordered__ab__group__add(X3223) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).
fof(i_0_1940,plain,
! [X3299,X3300,X3301,X3302,X3303] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3303,X3302,X3301)
| c_Orderings_Oord__class_Oless__eq(X3303,X3300,X3299)
| c_Groups_Ominus__class_Ominus(X3303,X3302,X3301) != c_Groups_Ominus__class_Ominus(X3303,X3300,X3299)
| ~ class_Groups_Oordered__ab__group__add(X3303) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3303,X3300,X3299)
| c_Orderings_Oord__class_Oless__eq(X3303,X3302,X3301)
| c_Groups_Ominus__class_Ominus(X3303,X3302,X3301) != c_Groups_Ominus__class_Ominus(X3303,X3300,X3299)
| ~ class_Groups_Oordered__ab__group__add(X3303) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).
fof(i_0_1941,plain,
! [X3916,X3917] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3917)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3917,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3916))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X3917),X3916) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add])]) ).
fof(i_0_1942,plain,
! [X3806,X3807] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3807)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3807,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3806))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X3807),X3806) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__add])]) ).
fof(i_0_1943,plain,
! [X4069,X4070] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4070,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4070),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4069)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4069) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4069,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4070),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4069)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4070)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4070,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4069,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4070),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4069)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4070,X4069))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4070,c_Int_OPls) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1366])])]) ).
fof(i_0_1944,plain,
! [X4740,X4741,X4742] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4742,X4741)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4742),X4740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4741),X4740)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).
fof(i_0_1945,plain,
! [X4737,X4738,X4739] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4739,X4738)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4737),X4739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4737),X4738)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).
fof(i_0_1946,plain,
! [X4226,X4227,X4228,X4229] :
( ~ class_Rings_Ocomm__semiring__1(X4229)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),X4228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),X4227),X4226)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),X4227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4229),X4228),X4226)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
fof(i_0_1947,plain,
! [X3418,X3419,X3420] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3420,X3419),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3420,X3418)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3419,X3418),
inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).
fof(i_0_1948,plain,
! [X3421,X3422,X3423] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3423,X3422),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3421,X3422)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3423,X3421),
inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).
fof(i_0_1949,plain,
! [X3132,X3133,X3134] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3134,X3133),X3132) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3134,X3132),X3133),
inference(variable_rename,[status(thm)],[fact_diff__commute]) ).
fof(i_0_1950,plain,
! [X3415,X3416,X3417] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3417,X3416),X3415) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3417,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3416,X3415)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(i_0_1951,plain,
! [X3865,X3866,X3867] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3867,X3866),X3865) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3867,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3866,X3865)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_1952,plain,
! [X2936,X2937,X2938] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2938,X2937),X2936) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2938,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2937,X2936)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_1953,plain,
! [X3868,X3869,X3870] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3870,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3869,X3868)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3869,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3870,X3868)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_1954,plain,
! [X2939,X2940,X2941] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2941,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2940,X2939)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2940,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2941,X2939)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_1955,plain,
! [X3826,X3827] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3827,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3826,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3827,X3826)
| X3827 = X3826 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3827,X3826)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3827,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3826,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( X3827 != X3826
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3827,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3826,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_1956,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_1367]) ).
cnf(i_0_1957,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_1368]) ).
cnf(i_0_1958,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_1369]) ).
cnf(i_0_1959,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_1370]) ).
fof(i_0_1960,plain,
! [X3828,X3829] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3829,c_Groups_Oone__class_Oone(tc_Int_Oint)),X3828)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3829,X3828) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3829,X3828)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3829,c_Groups_Oone__class_Oone(tc_Int_Oint)),X3828) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).
cnf(i_0_1961,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_1371]) ).
cnf(i_0_1962,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_1372]) ).
cnf(i_0_1963,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_1373]) ).
cnf(i_0_1964,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_1374]) ).
cnf(i_0_1965,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1375]) ).
cnf(i_0_1966,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_1376]) ).
fof(i_0_1967,plain,
! [X3824,X3825] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3825,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3824,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3825,X3824) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3825,X3824)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3825,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3824,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_1968,plain,
! [X3822,X3823] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3823,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3822,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3823,X3822) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3823,X3822)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3823,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3822,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_1969,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_1377]) ).
cnf(i_0_1970,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X1))),
inference(split_conjunct,[status(thm)],[i_0_1378]) ).
cnf(i_0_1971,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_1379]) ).
fof(i_0_1972,plain,
! [X4430,X4432,X4433,X4435] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk55_1(X4430))
| hBOOL(hAPP(X4430,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4432))) )
& ( ~ hBOOL(hAPP(X4430,esk55_1(X4430)))
| hBOOL(hAPP(X4430,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4432))) )
& ( ~ hBOOL(hAPP(X4433,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk56_1(X4433))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4435)
| hBOOL(hAPP(X4433,X4435)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I1_J])])])])])]) ).
fof(i_0_1973,plain,
! [X3839,X3840] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3840,X3839)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3840,X3839),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3840,X3839),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3840,X3839) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).
fof(i_0_1974,plain,
! [X3668,X3669] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3669,X3668)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3669,X3668),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,X3669,X3668),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3669,X3668) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff])]) ).
fof(i_0_1975,plain,
! [X3111,X3112] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3112,X3111))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3111,X3112) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3111,X3112)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3112,X3111)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
cnf(i_0_1976,plain,
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1321]) ).
cnf(i_0_1977,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_1380]) ).
fof(i_0_1978,plain,
! [X3496,X3497,X3498,X3499] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3499,X3498)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3497,X3498) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3499,X3496)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3497,X3496) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_1979,plain,
! [X3500,X3501,X3502] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3502,X3501),X3500)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3502,X3500) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_1980,plain,
! [X2804,X2805,X2806] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2806,X2804)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2806,X2805),X2804) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2805,X2804)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2806,X2805),X2804) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1381])])]) ).
fof(i_0_1981,plain,
! [X2807,X2808,X2809] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2809,X2808),X2807)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2809,X2807) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_1982,plain,
! [X2810,X2811,X2812] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2812,X2811),X2810)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2811,X2810) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_1983,plain,
! [X5309,X5310,X5311] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5311,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5310),X5309)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5311,X5310),X5309),
inference(variable_rename,[status(thm)],[fact_div__mult2__eq]) ).
cnf(i_0_1984,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_1382]) ).
cnf(i_0_1985,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_1383]) ).
cnf(i_0_1986,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_1384]) ).
cnf(i_0_1987,plain,
( X2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk29_2(X2,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1379]) ).
fof(i_0_1988,plain,
! [X3626,X3627,X3628] :
( ( X3627 = c_Groups_Ozero__class_Ozero(X3628)
| c_Groups_Oplus__class_Oplus(X3628,X3627,X3626) != c_Groups_Ozero__class_Ozero(X3628)
| ~ c_Orderings_Oord__class_Oless__eq(X3628,c_Groups_Ozero__class_Ozero(X3628),X3626)
| ~ c_Orderings_Oord__class_Oless__eq(X3628,c_Groups_Ozero__class_Ozero(X3628),X3627)
| ~ class_Groups_Oordered__comm__monoid__add(X3628) )
& ( X3626 = c_Groups_Ozero__class_Ozero(X3628)
| c_Groups_Oplus__class_Oplus(X3628,X3627,X3626) != c_Groups_Ozero__class_Ozero(X3628)
| ~ c_Orderings_Oord__class_Oless__eq(X3628,c_Groups_Ozero__class_Ozero(X3628),X3626)
| ~ c_Orderings_Oord__class_Oless__eq(X3628,c_Groups_Ozero__class_Ozero(X3628),X3627)
| ~ class_Groups_Oordered__comm__monoid__add(X3628) )
& ( X3627 != c_Groups_Ozero__class_Ozero(X3628)
| X3626 != c_Groups_Ozero__class_Ozero(X3628)
| c_Groups_Oplus__class_Oplus(X3628,X3627,X3626) = c_Groups_Ozero__class_Ozero(X3628)
| ~ c_Orderings_Oord__class_Oless__eq(X3628,c_Groups_Ozero__class_Ozero(X3628),X3626)
| ~ c_Orderings_Oord__class_Oless__eq(X3628,c_Groups_Ozero__class_Ozero(X3628),X3627)
| ~ class_Groups_Oordered__comm__monoid__add(X3628) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_1989,plain,
! [X3670,X3671,X3672,X3673] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3672,X3673),X3671,X3670)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3672,X3673),X3671,X3670)
| ~ class_Orderings_Oord(X3673) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3672,X3673),X3670,X3671)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3672,X3673),X3671,X3670)
| ~ class_Orderings_Oord(X3673) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3672,X3673),X3671,X3670)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3672,X3673),X3670,X3671)
| c_Orderings_Oord__class_Oless(tc_fun(X3672,X3673),X3671,X3670)
| ~ class_Orderings_Oord(X3673) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1385])])]) ).
cnf(i_0_1990,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_1386]) ).
fof(i_0_1991,plain,
! [X4056,X4057] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4057,X4056)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4056)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4057),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4056)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4057,X4056)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4057),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4056)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4057,X4056)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4057,X4056)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4057),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4056)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4056)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4057,X4056)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4057),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4056)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).
fof(i_0_1992,plain,
! [X5026,X5027] :
( ( ~ 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),X5027),X5026))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5027)
| X5026 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5027)
| 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),X5027),X5026)) )
& ( X5026 != 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),X5027),X5026)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
fof(i_0_1993,plain,
! [X5022,X5023] :
( ( ~ 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),X5023),X5022))
| X5022 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5023) )
& ( X5022 != 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),X5023),X5022)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5023)
| 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),X5023),X5022)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])]) ).
fof(i_0_1994,plain,
! [X5306,X5307,X5308] :
( ( X5308 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5308),X5307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5308),X5306)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5308 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5308),X5307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5308),X5306)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5307,X5306) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj])]) ).
fof(i_0_1995,plain,
! [X4196,X4197,X4198] :
( ~ class_Rings_Osemiring__1(X4198)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4197),X4196)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4198),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4198),X4197)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4198),X4196)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__mult])]) ).
fof(i_0_1996,plain,
! [X3914,X3915] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3915)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3915,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3914))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X3915),X3914) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__natfloor])]) ).
fof(i_0_1997,plain,
! [X3791,X3792] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3792),X3791)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3792,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3791))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3792) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3792,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3791))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3792),X3791)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3792) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq])])]) ).
fof(i_0_1998,plain,
! [X3907,X3908] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3907,c_RComplete_Onatfloor(X3908))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3907),X3908)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3908) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3907),X3908)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3907,c_RComplete_Onatfloor(X3908))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3908) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq])])]) ).
fof(i_0_1999,plain,
! [X5371,X5372] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk76_2(X5371,X5372))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5371)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5372) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk76_2(X5371,X5372)),X5372) = X5371
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5371)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5372) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth])])])]) ).
fof(i_0_2000,plain,
! [X5134,X5135,X5136] :
( ~ class_Rings_Olinordered__idom(X5136)
| c_Orderings_Oord__class_Oless__eq(X5136,c_Groups_Ozero__class_Ozero(X5136),hAPP(hAPP(c_Power_Opower__class_Opower(X5136),c_Groups_Oabs__class_Oabs(X5136,X5135)),X5134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).
cnf(i_0_2001,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X1)))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1338]) ).
cnf(i_0_2002,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_1387]) ).
fof(i_0_2003,plain,
! [X5093,X5094,X5095,X5096] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X5096),X5095),X5094) != hAPP(hAPP(c_Power_Opower__class_Opower(X5096),X5095),X5093)
| X5094 = X5093
| ~ c_Orderings_Oord__class_Oless(X5096,c_Groups_Oone__class_Oone(X5096),X5095)
| ~ class_Rings_Olinordered__semidom(X5096) )
& ( X5094 != X5093
| hAPP(hAPP(c_Power_Opower__class_Opower(X5096),X5095),X5094) = hAPP(hAPP(c_Power_Opower__class_Opower(X5096),X5095),X5093)
| ~ c_Orderings_Oord__class_Oless(X5096,c_Groups_Oone__class_Oone(X5096),X5095)
| ~ class_Rings_Olinordered__semidom(X5096) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_2004,plain,
! [X4836,X4837] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4837,c_Int_OPls)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4837)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4836)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4837,c_Int_OPls)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4837)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4836)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4837),X4836)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1388])]) ).
cnf(i_0_2005,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_1389]) ).
fof(i_0_2006,plain,
! [X4301,X4302,X4303] :
( ( ~ c_Orderings_Oord__class_Oless(X4303,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4303),X4302),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4303),X4301))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4302,X4301)
| ~ class_Rings_Olinordered__semidom(X4303) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4302,X4301)
| c_Orderings_Oord__class_Oless(X4303,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4303),X4302),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4303),X4301))
| ~ class_Rings_Olinordered__semidom(X4303) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff])])]) ).
fof(i_0_2007,plain,
! [X4295,X4296,X4297] :
( ~ class_Rings_Olinordered__semidom(X4297)
| ~ c_Orderings_Oord__class_Oless(X4297,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4297),X4296),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4297),X4295))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4296,X4295) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less])]) ).
fof(i_0_2008,plain,
! [X4304,X4305,X4306] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4306,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4306),X4305),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4306),X4304))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4305,X4304)
| ~ class_Rings_Olinordered__semidom(X4306) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4305,X4304)
| c_Orderings_Oord__class_Oless__eq(X4306,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4306),X4305),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4306),X4304))
| ~ class_Rings_Olinordered__semidom(X4306) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff])])]) ).
fof(i_0_2009,plain,
! [X5087,X5088,X5089] :
( ~ class_Rings_Olinordered__semidom(X5089)
| ~ c_Orderings_Oord__class_Oless(X5089,c_Groups_Ozero__class_Ozero(X5089),X5088)
| c_Orderings_Oord__class_Oless(X5089,c_Groups_Ozero__class_Ozero(X5089),hAPP(hAPP(c_Power_Opower__class_Opower(X5089),X5088),X5087)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_2010,plain,
! [X5080,X5081,X5082] :
( ~ class_Rings_Olinordered__semidom(X5082)
| ~ c_Orderings_Oord__class_Oless__eq(X5082,c_Groups_Ozero__class_Ozero(X5082),X5081)
| c_Orderings_Oord__class_Oless__eq(X5082,c_Groups_Ozero__class_Ozero(X5082),hAPP(hAPP(c_Power_Opower__class_Opower(X5082),X5081),X5080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).
fof(i_0_2011,plain,
! [X5090,X5091,X5092] :
( ~ class_Rings_Olinordered__semidom(X5092)
| ~ c_Orderings_Oord__class_Oless__eq(X5092,c_Groups_Oone__class_Oone(X5092),X5091)
| c_Orderings_Oord__class_Oless__eq(X5092,c_Groups_Oone__class_Oone(X5092),hAPP(hAPP(c_Power_Opower__class_Opower(X5092),X5091),X5090)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).
fof(i_0_2012,plain,
! [X3811] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3811)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3811,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X3811),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add__one])]) ).
fof(i_0_2013,plain,
! [X3808] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3808)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3808,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X3808),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_2014,plain,
! [X4371,X4372] :
( ~ class_Rings_Olinordered__ring(X4372)
| ~ c_Orderings_Oord__class_Oless(X4372,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4372),X4371),X4371),c_Groups_Ozero__class_Ozero(X4372)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1390])]) ).
cnf(i_0_2015,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X2)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1391]) ).
fof(i_0_2016,plain,
! [X4307,X4308,X4309] :
( ~ class_Rings_Osemiring__1(X4309)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4309),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4308,X4307)) = c_Groups_Oplus__class_Oplus(X4309,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4309),X4308),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4309),X4307)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__add])]) ).
fof(i_0_2017,plain,
! [X4058,X4059] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4059),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4058))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4059,X4058)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4059,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4059,X4058)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4059),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4058)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4059,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4059),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4058)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1392])])]) ).
fof(i_0_2018,plain,
! [X3820] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3820),X3820) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
fof(i_0_2019,plain,
! [X4031,X4032] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4032)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4031)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X4032,X4031)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).
fof(i_0_2020,plain,
! [X3135,X3136,X3137] :
( ~ class_Rings_Osemiring__1(X3137)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3137,X3136,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3135) = X3135 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])]) ).
fof(i_0_2021,plain,
! [X5193,X5194,X5195,X5196] : hAPP(hAPP(c_Power_Opower_Opower(X5196,X5195,X5194),X5193),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5195,
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).
cnf(i_0_2022,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_1393]) ).
cnf(i_0_2023,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_1394]) ).
cnf(i_0_2024,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_1395]) ).
fof(i_0_2025,plain,
! [X4436,X4437,X4439,X4440] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4437)
| ~ hBOOL(hAPP(X4436,X4437))
| hBOOL(hAPP(X4436,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk57_1(X4436)))) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk58_1(X4439))
| ~ hBOOL(hAPP(X4439,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4440))) )
& ( hBOOL(hAPP(X4439,esk58_1(X4439)))
| ~ hBOOL(hAPP(X4439,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4440))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I2_J])])])])])]) ).
fof(i_0_2026,plain,
! [X3831] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3831)
| 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),X3831)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).
fof(i_0_2027,plain,
! [X4186,X4187,X4188] :
( ~ class_Rings_Olinordered__idom(X4188)
| c_Groups_Oabs__class_Oabs(X4188,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4188),X4187),X4186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4188),c_Groups_Oabs__class_Oabs(X4188,X4187)),c_Groups_Oabs__class_Oabs(X4188,X4186)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).
cnf(i_0_2028,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1396]) ).
cnf(i_0_2029,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1397]) ).
cnf(i_0_2030,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1398]) ).
cnf(i_0_2031,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_1341]) ).
fof(i_0_2032,plain,
! [X3910] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3910,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X3910)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__add__one__gt]) ).
cnf(i_0_2033,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_1350]) ).
fof(i_0_2034,plain,
! [X4756,X4757] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4757)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4756)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4757),X4756)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).
fof(i_0_2035,plain,
! [X4729,X4730] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4730)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4729)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4730),X4729)),
inference(variable_rename,[status(thm)],[fact_zmult__int]) ).
fof(i_0_2036,plain,
! [X4731,X4732] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4732),X4731)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4732)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4731)),
inference(variable_rename,[status(thm)],[fact_int__mult]) ).
fof(i_0_2037,plain,
! [X4715,X4716] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4716),X4715)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X4716)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X4715)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__mult]) ).
fof(i_0_2038,plain,
! [X3942,X3943,X3944] :
( ~ class_RealVector_Oreal__normed__vector(X3944)
| c_RealVector_Onorm__class_Onorm(X3944,c_Groups_Ominus__class_Ominus(X3944,X3943,X3942)) = c_RealVector_Onorm__class_Onorm(X3944,c_Groups_Ominus__class_Ominus(X3944,X3942,X3943)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__commute])]) ).
fof(i_0_2039,plain,
! [X3724,X3725,X3726] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3726)
| c_Groups_Oabs__class_Oabs(X3726,c_Groups_Ominus__class_Ominus(X3726,X3725,X3724)) = c_Groups_Oabs__class_Oabs(X3726,c_Groups_Ominus__class_Ominus(X3726,X3724,X3725)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).
fof(i_0_2040,plain,
! [X4244,X4245,X4246] :
( ~ class_RealVector_Oreal__normed__div__algebra(X4246)
| c_RealVector_Onorm__class_Onorm(X4246,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4246),X4245),X4244)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4246,X4245)),c_RealVector_Onorm__class_Onorm(X4246,X4244)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])]) ).
cnf(i_0_2041,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1375]) ).
fof(i_0_2042,plain,
! [X3832,X3833] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3833,X3832)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3833,c_Groups_Oone__class_Oone(tc_Int_Oint)),X3832) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).
cnf(i_0_2043,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_1372]) ).
cnf(i_0_2044,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_1373]) ).
cnf(i_0_2045,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_1399]) ).
cnf(i_0_2046,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_1400]) ).
cnf(i_0_2047,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_1370]) ).
cnf(i_0_2048,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_1377]) ).
cnf(i_0_2049,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_1401]) ).
cnf(i_0_2050,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_1341]) ).
cnf(i_0_2051,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_1402]) ).
fof(i_0_2052,plain,
! [X3476,X3477] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3477,X3476),X3477),
inference(variable_rename,[status(thm)],[i_0_1403]) ).
fof(i_0_2053,plain,
! [X3478,X3479] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3479,X3478),X3478),
inference(variable_rename,[status(thm)],[i_0_1404]) ).
fof(i_0_2054,plain,
! [X5071,X5072,X5073] :
( ~ class_Rings_Osemiring__1(X5073)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5073),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5072),X5071)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5073),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5073),X5072)),X5071) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__power])]) ).
fof(i_0_2055,plain,
! [X3576,X3577] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3577,X3576)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3576,X3577),X3577) = X3576 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).
fof(i_0_2056,plain,
! [X3433,X3434] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3434,X3433)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3433,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3433,X3434)) = X3434 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).
fof(i_0_2057,plain,
! [X3584,X3585] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3585,X3584)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3585,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3584,X3585)) = X3584 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
fof(i_0_2058,plain,
! [X4121,X4122,X4123] :
( ~ class_Int_Onumber__ring(X4123)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4123),c_Int_Onumber__class_Onumber__of(X4123,X4122)),c_Int_Onumber__class_Onumber__of(X4123,X4121)) = c_Int_Onumber__class_Onumber__of(X4123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4122),X4121)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).
fof(i_0_2059,plain,
! [X4124,X4125,X4126] :
( ~ class_Int_Onumber__ring(X4126)
| c_Int_Onumber__class_Onumber__of(X4126,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4125),X4124)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4126),c_Int_Onumber__class_Onumber__of(X4126,X4125)),c_Int_Onumber__class_Onumber__of(X4126,X4124)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).
fof(i_0_2060,plain,
! [X2880,X2881,X2882,X2883,X2884] :
( ~ class_Orderings_Oord(X2884)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2883,X2884),X2882,X2881)
| c_Orderings_Oord__class_Oless__eq(X2884,hAPP(X2882,X2880),hAPP(X2881,X2880)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_2061,plain,
! [X2842,X2843,X2844,X2845,X2846] :
( ~ class_Orderings_Oord(X2846)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2845,X2846),X2844,X2843)
| c_Orderings_Oord__class_Oless__eq(X2846,hAPP(X2844,X2842),hAPP(X2843,X2842)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_2062,plain,
! [X3173,X3174,X3175] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3175,X3174)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3175,X3173),X3174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).
fof(i_0_2063,plain,
! [X3483,X3484,X3485] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3485,X3484)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3485,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3484,X3483)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_2064,plain,
! [X3470,X3471,X3472] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3472,X3471)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3472,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3471,X3470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_2065,plain,
! [X3486,X3487,X3488] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3488,X3487)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3488,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3486,X3487)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_2066,plain,
! [X3473,X3474,X3475] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3475,X3474)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3475,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3473,X3474)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_2067,plain,
! [X2953,X2954,X2955] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2955,X2954)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2955,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2954,X2953)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_2068,plain,
! [X2823,X2824,X2825] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2825,X2824)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2825,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2824,X2823)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_2069,plain,
! [X2950,X2951,X2952] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2952,X2951)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2952,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2950,X2951)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_2070,plain,
! [X2820,X2821,X2822] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2822,X2821)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2822,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2820,X2821)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
cnf(i_0_2071,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_1383]) ).
cnf(i_0_2072,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_1383]) ).
cnf(i_0_2073,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_1384]) ).
cnf(i_0_2074,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_1384]) ).
fof(i_0_2075,plain,
! [X4456,X4457] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4457),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4456))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4457,X4456) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4457,X4456)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4457),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4456)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__int])]) ).
fof(i_0_2076,plain,
! [X4454,X4455] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4455),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4454))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4455,X4454) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4455,X4454)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4455),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4454)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J])]) ).
fof(i_0_2077,plain,
! [X3273,X3274] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3274),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3273))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3274,X3273) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3274,X3273)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3274),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3273)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff])]) ).
fof(i_0_2078,plain,
! [X4460,X4461] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4461),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4460))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4461,X4460) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4461,X4460)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4461),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4460)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__int])]) ).
fof(i_0_2079,plain,
! [X4458,X4459] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4459),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4458))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4459,X4458) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4459,X4458)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4459),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4458)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J])]) ).
fof(i_0_2080,plain,
! [X2944,X2945] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2945),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2944))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2945,X2944) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2945,X2944)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2945),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2944)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff])]) ).
fof(i_0_2081,plain,
! [X5320,X5321] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5321),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5320)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5321,X5320)),
inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).
fof(i_0_2082,plain,
! [X4481,X4482] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4482),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4481)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4482,X4481)),
inference(variable_rename,[status(thm)],[fact_zadd__int]) ).
fof(i_0_2083,plain,
! [X4479,X4480] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4480),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4479)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4480,X4479)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).
fof(i_0_2084,plain,
! [X5322,X5323] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5323,X5322)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5323),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5322)),
inference(variable_rename,[status(thm)],[fact_zdiv__int]) ).
fof(i_0_2085,plain,
! [X2948,X2949] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2949,X2948)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2949),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2948)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__add]) ).
fof(i_0_2086,plain,
! [X5046,X5047] : 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X5047)),X5046)),
inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(i_0_2087,plain,
! [X4919] :
( ( 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),X4919),X4919))
| X4919 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4919 != 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),X4919),X4919)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1405])]) ).
fof(i_0_2088,plain,
! [X4883,X4884,X4885] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4885),X4884) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4885),X4883)
| X4884 = X4883
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4885) )
& ( X4884 != X4883
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4885),X4884) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4885),X4883)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4885) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
cnf(i_0_2089,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Nat_OSuc(X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1406]) ).
fof(i_0_2090,plain,
! [X3732,X3733,X3734] :
( ( ~ c_Orderings_Oord__class_Oless(X3734,c_Int_Onumber__class_Onumber__of(X3734,X3733),c_Int_Onumber__class_Onumber__of(X3734,X3732))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3733,X3732)
| ~ class_Int_Onumber__ring(X3734)
| ~ class_Rings_Olinordered__idom(X3734) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3733,X3732)
| c_Orderings_Oord__class_Oless(X3734,c_Int_Onumber__class_Onumber__of(X3734,X3733),c_Int_Onumber__class_Onumber__of(X3734,X3732))
| ~ class_Int_Onumber__ring(X3734)
| ~ class_Rings_Olinordered__idom(X3734) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).
fof(i_0_2091,plain,
! [X3729,X3730,X3731] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3731,c_Int_Onumber__class_Onumber__of(X3731,X3730),c_Int_Onumber__class_Onumber__of(X3731,X3729))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3730,X3729)
| ~ class_Int_Onumber__ring(X3731)
| ~ class_Rings_Olinordered__idom(X3731) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3730,X3729)
| c_Orderings_Oord__class_Oless__eq(X3731,c_Int_Onumber__class_Onumber__of(X3731,X3730),c_Int_Onumber__class_Onumber__of(X3731,X3729))
| ~ class_Int_Onumber__ring(X3731)
| ~ class_Rings_Olinordered__idom(X3731) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).
fof(i_0_2092,plain,
! [X5024,X5025] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5025)
| 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),X5025),X5024)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).
fof(i_0_2093,plain,
! [X3198,X3199,X3200,X3201] :
( ~ class_Orderings_Opreorder(X3201)
| ~ c_Orderings_Oord__class_Oless(X3201,X3200,X3199)
| ~ c_Orderings_Oord__class_Oless(X3201,X3199,X3198)
| c_Orderings_Oord__class_Oless(X3201,X3200,X3198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_2094,plain,
! [X3369,X3370,X3371,X3372] :
( ~ class_Orderings_Opreorder(X3372)
| ~ c_Orderings_Oord__class_Oless__eq(X3372,X3371,X3370)
| ~ c_Orderings_Oord__class_Oless(X3372,X3370,X3369)
| c_Orderings_Oord__class_Oless(X3372,X3371,X3369) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_2095,plain,
! [X3361,X3362,X3363,X3364] :
( ~ class_Orderings_Opreorder(X3364)
| ~ c_Orderings_Oord__class_Oless(X3364,X3363,X3362)
| ~ c_Orderings_Oord__class_Oless__eq(X3364,X3362,X3361)
| c_Orderings_Oord__class_Oless(X3364,X3363,X3361) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_2096,plain,
! [X3202,X3203,X3204,X3205] :
( ~ class_Orderings_Oorder(X3205)
| ~ c_Orderings_Oord__class_Oless(X3205,X3204,X3203)
| ~ c_Orderings_Oord__class_Oless(X3205,X3202,X3204)
| c_Orderings_Oord__class_Oless(X3205,X3202,X3203) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_2097,plain,
! [X3373,X3374,X3375,X3376] :
( ~ class_Orderings_Oorder(X3376)
| ~ c_Orderings_Oord__class_Oless__eq(X3376,X3375,X3374)
| ~ c_Orderings_Oord__class_Oless(X3376,X3373,X3375)
| c_Orderings_Oord__class_Oless(X3376,X3373,X3374) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_2098,plain,
! [X3365,X3366,X3367,X3368] :
( ~ class_Orderings_Oorder(X3368)
| ~ c_Orderings_Oord__class_Oless(X3368,X3367,X3366)
| ~ c_Orderings_Oord__class_Oless__eq(X3368,X3365,X3367)
| c_Orderings_Oord__class_Oless(X3368,X3365,X3366) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_2099,plain,
! [X2854,X2855,X2856,X2857] :
( ~ class_Orderings_Opreorder(X2857)
| ~ c_Orderings_Oord__class_Oless__eq(X2857,X2856,X2855)
| ~ c_Orderings_Oord__class_Oless__eq(X2857,X2855,X2854)
| c_Orderings_Oord__class_Oless__eq(X2857,X2856,X2854) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_2100,plain,
! [X2847,X2848,X2849,X2850] :
( ~ class_Orderings_Oorder(X2850)
| ~ c_Orderings_Oord__class_Oless__eq(X2850,X2849,X2848)
| ~ c_Orderings_Oord__class_Oless__eq(X2850,X2847,X2849)
| c_Orderings_Oord__class_Oless__eq(X2850,X2847,X2848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_2101,plain,
! [X5331,X5332] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5332)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5332),X5331),X5332) = X5331 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])]) ).
fof(i_0_2102,plain,
! [X5329,X5330] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5330)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5329),X5330),X5330) = X5329 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m])]) ).
fof(i_0_2103,plain,
! [X3739,X3740,X3741] :
( ~ class_Int_Onumber__ring(X3741)
| c_Groups_Oplus__class_Oplus(X3741,c_Int_Onumber__class_Onumber__of(X3741,X3740),c_Int_Onumber__class_Onumber__of(X3741,X3739)) = c_Int_Onumber__class_Onumber__of(X3741,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3740,X3739)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).
fof(i_0_2104,plain,
! [X3745,X3746,X3747] :
( ~ class_Int_Onumber__ring(X3747)
| c_Int_Onumber__class_Onumber__of(X3747,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3746,X3745)) = c_Groups_Ominus__class_Ominus(X3747,c_Int_Onumber__class_Onumber__of(X3747,X3746),c_Int_Onumber__class_Onumber__of(X3747,X3745)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])]) ).
fof(i_0_2105,plain,
! [X3742,X3743,X3744] :
( ~ class_Int_Onumber__ring(X3744)
| c_Int_Onumber__class_Onumber__of(X3744,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3743,X3742)) = c_Groups_Oplus__class_Oplus(X3744,c_Int_Onumber__class_Onumber__of(X3744,X3743),c_Int_Onumber__class_Onumber__of(X3744,X3742)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).
cnf(i_0_2106,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_1407]) ).
cnf(i_0_2107,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1408]) ).
fof(i_0_2108,plain,
! [X5235,X5236] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5236,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),X5236)
| X5235 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5236,X5235) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5235,X5236)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5236)
| X5235 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5236,X5235) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5236,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5236,X5235)
| X5235 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5236,X5235) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5235,X5236)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5236,X5235)
| X5235 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5236,X5235) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X5235 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5236,X5235) = 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),X5236)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5236,X5235)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5236,X5235) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5236,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5235,X5236)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5236,X5235) = 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_2109,plain,
! [X5222,X5223] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5223)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5223,X5222)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5223,X5222) = 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_2110,plain,
! [X5213,X5214] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5214,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5213,X5214)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5214,X5213) = 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_2111,plain,
! [X5068,X5069,X5070] :
( ~ class_Rings_Olinordered__idom(X5070)
| c_Groups_Oabs__class_Oabs(X5070,hAPP(hAPP(c_Power_Opower__class_Opower(X5070),X5069),X5068)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5070),c_Groups_Oabs__class_Oabs(X5070,X5069)),X5068) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).
cnf(i_0_2112,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_1386]) ).
cnf(i_0_2113,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_1386]) ).
fof(i_0_2114,plain,
! [X3573,X3574,X3575] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3574,X3575) != X3573
| X3574 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3573,X3575)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3575,X3574) )
& ( X3574 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3573,X3575)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3574,X3575) = X3573
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3575,X3574) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).
fof(i_0_2115,plain,
! [X4298,X4299,X4300] :
( ~ class_Rings_Olinordered__semidom(X4300)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4299,X4298)
| c_Orderings_Oord__class_Oless(X4300,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4300),X4299),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4300),X4298)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less])]) ).
fof(i_0_2116,plain,
! [X4473,X4474,X4476,X4477,X4478] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4474,X4473)
| X4473 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4474,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk59_2(X4473,X4474))) )
& ( X4476 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4477,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4478))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4477,X4476) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__iff__zadd])])])])]) ).
fof(i_0_2117,plain,
! [X4962,X4963,X4964] :
( ~ class_RealVector_Oreal__normed__div__algebra(X4964)
| c_RealVector_Onorm__class_Onorm(X4964,hAPP(hAPP(c_Power_Opower__class_Opower(X4964),X4963),X4962)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4964,X4963)),X4962) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power])]) ).
fof(i_0_2118,plain,
! [X3859,X3860,X3861] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3861,X3860)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3860,X3859)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3861,X3859) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).
fof(i_0_2119,plain,
! [X2974,X2975,X2976] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2976,X2975)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2975,X2974)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2976,X2974) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(i_0_2120,plain,
! [X2786,X2787,X2788] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2788,X2787)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2787,X2786)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2788,X2786) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
cnf(i_0_2121,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_1369]) ).
fof(i_0_2122,plain,
! [X4657,X4658] :
( ( ~ c_Orderings_Oord__class_Oless(X4658,c_Groups_Ozero__class_Ozero(X4658),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4658),X4657))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4657)
| ~ class_Rings_Olinordered__semidom(X4658) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4657)
| c_Orderings_Oord__class_Oless(X4658,c_Groups_Ozero__class_Ozero(X4658),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4658),X4657))
| ~ class_Rings_Olinordered__semidom(X4658) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff])])]) ).
cnf(i_0_2123,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Int_Osucc(X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1409]) ).
fof(i_0_2124,plain,
! [X4119,X4120] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4120)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4119)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4120),X4119)),
inference(variable_rename,[status(thm)],[fact_times__numeral__code_I5_J]) ).
fof(i_0_2125,plain,
! [X5018,X5019] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5019)),X5018) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5019),X5018)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).
fof(i_0_2126,plain,
! [X5014,X5015] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5015)),X5014) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5015),X5014)),
inference(variable_rename,[status(thm)],[fact_zpower__int]) ).
fof(i_0_2127,plain,
! [X5034,X5035] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5035)),X5034) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5035),X5034)),
inference(variable_rename,[status(thm)],[fact_power__real__of__nat]) ).
fof(i_0_2128,plain,
! [X5016,X5017] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5017),X5016)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5017)),X5016),
inference(variable_rename,[status(thm)],[fact_int__power]) ).
fof(i_0_2129,plain,
! [X5036,X5037] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5037),X5036)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5037)),X5036),
inference(variable_rename,[status(thm)],[fact_real__of__nat__power]) ).
fof(i_0_2130,plain,
! [X3987,X3988] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987))
| c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987))
| X3988 = X3987
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( X3988 != X3987
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987))
| c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( X3988 != X3987
| c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( X3988 != X3987
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987))
| c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) )
& ( X3988 != X3987
| c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3988) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3988) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3987) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1410])])]) ).
cnf(i_0_2131,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_1351]) ).
cnf(i_0_2132,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_1352]) ).
cnf(i_0_2133,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[i_0_1411]) ).
cnf(i_0_2134,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[i_0_1412]) ).
fof(i_0_2135,plain,
! [X3852,X3853] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3853),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3852)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3853,X3852)),
inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).
cnf(i_0_2136,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_1383]) ).
cnf(i_0_2137,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_1383]) ).
cnf(i_0_2138,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_1384]) ).
cnf(i_0_2139,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_1384]) ).
fof(i_0_2140,plain,
! [X3804] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3804))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
fof(i_0_2141,plain,
! [X3240,X3241] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3241,X3240)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3240,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3241,X3240)) = X3241 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1413])]) ).
fof(i_0_2142,plain,
! [X3835,X3836] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3836),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3835))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3836,X3835) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3836,X3835)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3836),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3835)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).
fof(i_0_2143,plain,
! [X3854,X3855] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3855),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3854))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3855,X3854) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3855,X3854)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3855),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3854)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).
fof(i_0_2144,plain,
! [X3546,X3547,X3548,X3549] :
( ( ~ c_SEQ_Osubseq(X3546)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3547,X3548)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3546,X3547),hAPP(X3546,X3548)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk27_1(X3549),esk28_1(X3549))
| c_SEQ_Osubseq(X3549) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3549,esk27_1(X3549)),hAPP(X3549,esk28_1(X3549)))
| c_SEQ_Osubseq(X3549) ) ),
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_subseq__def])])])])])]) ).
fof(i_0_2145,plain,
! [X3913] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3913,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X3913))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__gt__diff__one]) ).
fof(i_0_2146,plain,
! [X3322,X3323,X3324] :
( ( c_Orderings_Oord__class_Oless__eq(X3324,X3323,X3322)
| ~ c_Orderings_Oord__class_Oless(X3324,X3323,X3322)
| ~ class_Orderings_Opreorder(X3324) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3324,X3322,X3323)
| ~ c_Orderings_Oord__class_Oless(X3324,X3323,X3322)
| ~ class_Orderings_Opreorder(X3324) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3324,X3323,X3322)
| c_Orderings_Oord__class_Oless__eq(X3324,X3322,X3323)
| c_Orderings_Oord__class_Oless(X3324,X3323,X3322)
| ~ class_Orderings_Opreorder(X3324) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1414])])]) ).
fof(i_0_2147,plain,
! [X4066,X4067] :
( ( ~ c_Orderings_Oord__class_Oless(X4067,c_Groups_Ozero__class_Ozero(X4067),c_Int_Onumber__class_Onumber__of(X4067,X4066))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4066)
| ~ class_Int_Onumber__ring(X4067)
| ~ class_Rings_Olinordered__idom(X4067) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4066)
| c_Orderings_Oord__class_Oless(X4067,c_Groups_Ozero__class_Ozero(X4067),c_Int_Onumber__class_Onumber__of(X4067,X4066))
| ~ class_Int_Onumber__ring(X4067)
| ~ class_Rings_Olinordered__idom(X4067) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).
fof(i_0_2148,plain,
! [X4062,X4063] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4063,c_Groups_Ozero__class_Ozero(X4063),c_Int_Onumber__class_Onumber__of(X4063,X4062))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4062)
| ~ class_Int_Onumber__ring(X4063)
| ~ class_Rings_Olinordered__idom(X4063) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4062)
| c_Orderings_Oord__class_Oless__eq(X4063,c_Groups_Ozero__class_Ozero(X4063),c_Int_Onumber__class_Onumber__of(X4063,X4062))
| ~ class_Int_Onumber__ring(X4063)
| ~ class_Rings_Olinordered__idom(X4063) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).
fof(i_0_2149,plain,
! [X4064,X4065] :
( ( ~ c_Orderings_Oord__class_Oless(X4065,c_Int_Onumber__class_Onumber__of(X4065,X4064),c_Groups_Ozero__class_Ozero(X4065))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4064,c_Int_OPls)
| ~ class_Int_Onumber__ring(X4065)
| ~ class_Rings_Olinordered__idom(X4065) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4064,c_Int_OPls)
| c_Orderings_Oord__class_Oless(X4065,c_Int_Onumber__class_Onumber__of(X4065,X4064),c_Groups_Ozero__class_Ozero(X4065))
| ~ class_Int_Onumber__ring(X4065)
| ~ class_Rings_Olinordered__idom(X4065) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).
fof(i_0_2150,plain,
! [X4060,X4061] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4061,c_Int_Onumber__class_Onumber__of(X4061,X4060),c_Groups_Ozero__class_Ozero(X4061))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4060,c_Int_OPls)
| ~ class_Int_Onumber__ring(X4061)
| ~ class_Rings_Olinordered__idom(X4061) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4060,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(X4061,c_Int_Onumber__class_Onumber__of(X4061,X4060),c_Groups_Ozero__class_Ozero(X4061))
| ~ class_Int_Onumber__ring(X4061)
| ~ class_Rings_Olinordered__idom(X4061) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).
cnf(i_0_2151,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_1407]) ).
fof(i_0_2152,plain,
! [X3653] :
( ~ class_Rings_Olinordered__semidom(X3653)
| c_Orderings_Oord__class_Oless(X3653,c_Groups_Ozero__class_Ozero(X3653),c_Groups_Oplus__class_Oplus(X3653,c_Groups_Oone__class_Oone(X3653),c_Groups_Oone__class_Oone(X3653))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_2153,plain,
! [X4536,X4537] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4537),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4536)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4537,X4536)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).
fof(i_0_2154,plain,
! [X4659] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4659))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4659) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4659)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4659)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])]) ).
fof(i_0_2155,plain,
! [X3683] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3683))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3683) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3683)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3683)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff])]) ).
fof(i_0_2156,plain,
! [X3789,X3790] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3790,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3789))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3790),X3789) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le])]) ).
fof(i_0_2157,plain,
! [X3885,X3886] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3886),X3885)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3886,c_RComplete_Onatfloor(X3885)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor])]) ).
cnf(i_0_2158,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_1415]) ).
fof(i_0_2159,plain,
! [X3228,X3229,X3230] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3229,X3230)
| hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| X3230 = X3229
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3230,X3229) )
& ( ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| X3230 = X3229
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3230,X3229) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3229,X3230)
| hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3230,X3229) )
& ( ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3230,X3229) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3229,X3230)
| hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| X3230 = X3229
| ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230)) )
& ( ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| X3230 = X3229
| ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3229,X3230)
| hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230)) )
& ( ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230))
| ~ hBOOL(hAPP(hAPP(X3228,X3229),X3230)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_2160,plain,
! [X5048,X5049] :
( X5049 != hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X5049))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5049),X5048)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X5049)),X5048) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__power])]) ).
fof(i_0_2161,plain,
! [X4184,X4185] :
( ~ class_Rings_Olinordered__idom(X4185)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4185),c_Groups_Oabs__class_Oabs(X4185,X4184)),c_Groups_Oabs__class_Oabs(X4185,X4184)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4185),X4184),X4184) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).
fof(i_0_2162,plain,
! [X3716,X3717,X3718] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3718)
| ~ c_Orderings_Oord__class_Oless__eq(X3718,c_Groups_Oabs__class_Oabs(X3718,X3717),X3716)
| c_Orderings_Oord__class_Oless__eq(X3718,X3717,X3716) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).
fof(i_0_2163,plain,
! [X4085,X4086] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4085))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4086),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4085)) = c_Int_Onumber__class_Onumber__of(X4086,X4085)
| ~ class_Int_Onumber__ring(X4086) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4085))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4086),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4085)) = c_Groups_Ozero__class_Ozero(X4086)
| ~ class_Int_Onumber__ring(X4086) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1416])])]) ).
fof(i_0_2164,plain,
! [X4035,X4036,X4038] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk53_2(X4035,X4036))
| ~ c_SEQ_OBseq(X4036,X4035)
| ~ class_RealVector_Oreal__normed__vector(X4036) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4036,hAPP(X4035,X4038)),esk53_2(X4035,X4036))
| ~ c_SEQ_OBseq(X4036,X4035)
| ~ class_RealVector_Oreal__normed__vector(X4036) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_BseqD])])])])]) ).
fof(i_0_2165,plain,
! [X3884] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3884)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X3884)),X3884) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__natfloor__le])]) ).
fof(i_0_2166,plain,
! [X3214,X3215,X3216,X3217,X3218] :
( ( X3217 != X3216
| X3215 = X3214
| c_Groups_Ominus__class_Ominus(X3218,X3217,X3216) != c_Groups_Ominus__class_Ominus(X3218,X3215,X3214)
| ~ class_Groups_Oab__group__add(X3218) )
& ( X3215 != X3214
| X3217 = X3216
| c_Groups_Ominus__class_Ominus(X3218,X3217,X3216) != c_Groups_Ominus__class_Ominus(X3218,X3215,X3214)
| ~ class_Groups_Oab__group__add(X3218) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).
cnf(i_0_2167,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_1383]) ).
cnf(i_0_2168,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_1384]) ).
fof(i_0_2169,plain,
! [X3349,X3350,X3351] :
( ( c_Orderings_Oord__class_Oless(X3351,X3350,X3349)
| X3350 = X3349
| ~ c_Orderings_Oord__class_Oless__eq(X3351,X3350,X3349)
| ~ class_Orderings_Olinorder(X3351) )
& ( X3350 != X3349
| ~ c_Orderings_Oord__class_Oless(X3351,X3350,X3349)
| ~ c_Orderings_Oord__class_Oless__eq(X3351,X3350,X3349)
| ~ class_Orderings_Olinorder(X3351) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1417])])]) ).
fof(i_0_2170,plain,
! [X2888,X2889,X2890] :
( ( c_Orderings_Oord__class_Oless__eq(X2890,X2889,X2888)
| X2889 != X2888
| ~ class_Orderings_Oorder(X2890) )
& ( c_Orderings_Oord__class_Oless__eq(X2890,X2888,X2889)
| X2889 != X2888
| ~ class_Orderings_Oorder(X2890) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2890,X2889,X2888)
| ~ c_Orderings_Oord__class_Oless__eq(X2890,X2888,X2889)
| X2889 = X2888
| ~ class_Orderings_Oorder(X2890) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_2171,plain,
! [X2877,X2878,X2879] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2879,X2877,X2878)
| X2877 = X2878
| ~ c_Orderings_Oord__class_Oless__eq(X2879,X2878,X2877)
| ~ class_Orderings_Oorder(X2879) )
& ( X2877 != X2878
| c_Orderings_Oord__class_Oless__eq(X2879,X2877,X2878)
| ~ c_Orderings_Oord__class_Oless__eq(X2879,X2878,X2877)
| ~ class_Orderings_Oorder(X2879) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_2172,plain,
! [X2858,X2859,X2860] :
( ~ class_Orderings_Oorder(X2860)
| ~ c_Orderings_Oord__class_Oless__eq(X2860,X2859,X2858)
| ~ c_Orderings_Oord__class_Oless__eq(X2860,X2858,X2859)
| X2859 = X2858 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_2173,plain,
! [X2851,X2852,X2853] :
( ~ class_Orderings_Oorder(X2853)
| ~ c_Orderings_Oord__class_Oless__eq(X2853,X2852,X2851)
| ~ c_Orderings_Oord__class_Oless__eq(X2853,X2851,X2852)
| X2851 = X2852 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_2174,plain,
! [X3655,X3656] :
( ~ class_Rings_Olinordered__semidom(X3656)
| c_Orderings_Oord__class_Oless(X3656,X3655,c_Groups_Oplus__class_Oplus(X3656,X3655,c_Groups_Oone__class_Oone(X3656))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_2175,plain,
! [X2912,X2913,X2914,X2915] :
( ( c_Groups_Oplus__class_Oplus(X2915,X2914,X2913) != c_Groups_Oplus__class_Oplus(X2915,X2912,X2913)
| X2914 = X2912
| ~ class_Groups_Ocancel__semigroup__add(X2915) )
& ( X2914 != X2912
| c_Groups_Oplus__class_Oplus(X2915,X2914,X2913) = c_Groups_Oplus__class_Oplus(X2915,X2912,X2913)
| ~ class_Groups_Ocancel__semigroup__add(X2915) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_2176,plain,
! [X2900,X2901,X2902,X2903] :
( ~ class_Groups_Ocancel__semigroup__add(X2903)
| c_Groups_Oplus__class_Oplus(X2903,X2902,X2901) != c_Groups_Oplus__class_Oplus(X2903,X2900,X2901)
| X2902 = X2900 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_2177,plain,
! [X2904,X2905,X2906,X2907] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X2907)
| c_Groups_Oplus__class_Oplus(X2907,X2906,X2905) != c_Groups_Oplus__class_Oplus(X2907,X2906,X2904)
| X2905 = X2904 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_2178,plain,
! [X2916,X2917,X2918,X2919] :
( ( c_Groups_Oplus__class_Oplus(X2919,X2918,X2917) != c_Groups_Oplus__class_Oplus(X2919,X2918,X2916)
| X2917 = X2916
| ~ class_Groups_Ocancel__semigroup__add(X2919) )
& ( X2917 != X2916
| c_Groups_Oplus__class_Oplus(X2919,X2918,X2917) = c_Groups_Oplus__class_Oplus(X2919,X2918,X2916)
| ~ class_Groups_Ocancel__semigroup__add(X2919) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_2179,plain,
! [X2908,X2909,X2910,X2911] :
( ~ class_Groups_Ocancel__semigroup__add(X2911)
| c_Groups_Oplus__class_Oplus(X2911,X2910,X2909) != c_Groups_Oplus__class_Oplus(X2911,X2910,X2908)
| X2909 = X2908 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_2180,plain,
! [X4534,X4535] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4535),X4534)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4535) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1])]) ).
fof(i_0_2181,plain,
! [X3179,X3180,X3181] :
( ~ class_Orderings_Oorder(X3181)
| ~ c_Orderings_Oord__class_Oless(X3181,X3180,X3179)
| ~ c_Orderings_Oord__class_Oless(X3181,X3179,X3180) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1418])]) ).
fof(i_0_2182,plain,
! [X3105,X3106,X3107] :
( ( c_Orderings_Oord__class_Oless(X3107,X3106,X3105)
| c_Orderings_Oord__class_Oless(X3107,X3105,X3106)
| X3106 = X3105
| ~ class_Orderings_Olinorder(X3107) )
& ( ~ c_Orderings_Oord__class_Oless(X3107,X3105,X3106)
| ~ c_Orderings_Oord__class_Oless(X3107,X3106,X3105)
| ~ class_Orderings_Olinorder(X3107) )
& ( X3106 != X3105
| ~ c_Orderings_Oord__class_Oless(X3107,X3106,X3105)
| ~ class_Orderings_Olinorder(X3107) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1419])])]) ).
fof(i_0_2183,plain,
! [X3343,X3344,X3345] :
( ~ class_Orderings_Olinorder(X3345)
| ~ c_Orderings_Oord__class_Oless__eq(X3345,X3344,X3343)
| ~ c_Orderings_Oord__class_Oless(X3345,X3343,X3344) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1420])]) ).
fof(i_0_2184,plain,
! [X3310,X3311,X3312] :
( ( c_Orderings_Oord__class_Oless(X3312,X3311,X3310)
| c_Orderings_Oord__class_Oless__eq(X3312,X3310,X3311)
| ~ class_Orderings_Olinorder(X3312) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3312,X3310,X3311)
| ~ c_Orderings_Oord__class_Oless(X3312,X3311,X3310)
| ~ class_Orderings_Olinorder(X3312) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1421])])]) ).
fof(i_0_2185,plain,
! [X3313,X3314,X3315] :
( ( c_Orderings_Oord__class_Oless__eq(X3315,X3314,X3313)
| c_Orderings_Oord__class_Oless(X3315,X3313,X3314)
| ~ class_Orderings_Olinorder(X3315) )
& ( ~ c_Orderings_Oord__class_Oless(X3315,X3313,X3314)
| ~ c_Orderings_Oord__class_Oless__eq(X3315,X3314,X3313)
| ~ class_Orderings_Olinorder(X3315) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1422])])]) ).
fof(i_0_2186,plain,
! [X3209,X3210,X3211] :
( ~ class_Orderings_Opreorder(X3211)
| ~ c_Orderings_Oord__class_Oless(X3211,X3210,X3209)
| ~ c_Orderings_Oord__class_Oless(X3211,X3209,X3210) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1423])]) ).
fof(i_0_2187,plain,
! [X3176,X3177,X3178] :
( ~ class_Orderings_Opreorder(X3178)
| ~ c_Orderings_Oord__class_Oless(X3178,X3177,X3176)
| ~ c_Orderings_Oord__class_Oless(X3178,X3176,X3177) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1424])]) ).
fof(i_0_2188,plain,
! [X3164,X3165,X3166] :
( ~ class_Orderings_Opreorder(X3166)
| ~ c_Orderings_Oord__class_Oless(X3166,X3165,X3164)
| ~ c_Orderings_Oord__class_Oless(X3166,X3164,X3165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1425])]) ).
fof(i_0_2189,plain,
! [X3161,X3162,X3163] :
( ~ class_Orderings_Opreorder(X3163)
| ~ c_Orderings_Oord__class_Oless(X3163,X3162,X3161)
| ~ c_Orderings_Oord__class_Oless(X3163,X3161,X3162) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1426])]) ).
cnf(i_0_2190,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1427]) ).
cnf(i_0_2191,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1428]) ).
fof(i_0_2192,plain,
! [X4991,X4992,X4993] :
( ( X4992 = c_Groups_Ozero__class_Ozero(X4993)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4993),X4992),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4991)) != c_Groups_Ozero__class_Ozero(X4993)
| ~ class_Power_Opower(X4993)
| ~ class_Rings_Omult__zero(X4993)
| ~ class_Rings_Ono__zero__divisors(X4993)
| ~ class_Rings_Ozero__neq__one(X4993) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4991) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4993),X4992),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4991)) != c_Groups_Ozero__class_Ozero(X4993)
| ~ class_Power_Opower(X4993)
| ~ class_Rings_Omult__zero(X4993)
| ~ class_Rings_Ono__zero__divisors(X4993)
| ~ class_Rings_Ozero__neq__one(X4993) )
& ( X4992 != c_Groups_Ozero__class_Ozero(X4993)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4991) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4993),X4992),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4991)) = c_Groups_Ozero__class_Ozero(X4993)
| ~ class_Power_Opower(X4993)
| ~ class_Rings_Omult__zero(X4993)
| ~ class_Rings_Ono__zero__divisors(X4993)
| ~ class_Rings_Ozero__neq__one(X4993) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff__number__of])])]) ).
fof(i_0_2193,plain,
! [X3212,X3213] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3213,X3212) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3212,X3213) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3213 = X3212 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).
fof(i_0_2194,plain,
! [X4068] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4068))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4068) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4068)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4068)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).
cnf(i_0_2195,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_1387]) ).
fof(i_0_2196,plain,
! [X4805,X4806] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X4806,X4805)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X4806)),c_Complex_Oexpi(X4805)),
inference(variable_rename,[status(thm)],[fact_expi__add]) ).
fof(i_0_2197,plain,
! [X5264,X5265,X5266] :
( ~ class_Divides_Osemiring__div(X5266)
| X5265 = c_Groups_Ozero__class_Ozero(X5266)
| c_Divides_Odiv__class_Odiv(X5266,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5266),X5265),X5264),X5265) = X5264 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id])]) ).
fof(i_0_2198,plain,
! [X5267,X5268,X5269] :
( ~ class_Divides_Osemiring__div(X5269)
| X5268 = c_Groups_Ozero__class_Ozero(X5269)
| c_Divides_Odiv__class_Odiv(X5269,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5269),X5267),X5268),X5268) = X5267 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])]) ).
fof(i_0_2199,plain,
! [X4312,X4313] :
( ~ class_Rings_Olinordered__ring(X4313)
| c_Orderings_Oord__class_Oless__eq(X4313,c_Groups_Ozero__class_Ozero(X4313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4313),X4312),X4312)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).
fof(i_0_2200,plain,
! [X3857,X3858] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3858,X3857)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3857,X3858)
| X3858 = X3857 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).
fof(i_0_2201,plain,
! [X2972,X2973] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2973,X2972)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2972,X2973)
| X2973 = X2972 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
fof(i_0_2202,plain,
! [X2789,X2790] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2790,X2789)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2789,X2790)
| X2790 = X2789 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
cnf(i_0_2203,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X1,
inference(split_conjunct,[status(thm)],[i_0_1429]) ).
fof(i_0_2204,plain,
! [X3307,X3308,X3309] :
( ~ class_Groups_Ogroup__add(X3309)
| c_Groups_Ominus__class_Ominus(X3309,c_Groups_Oplus__class_Oplus(X3309,X3308,X3307),X3307) = X3308 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(i_0_2205,plain,
! [X3304,X3305,X3306] :
( ~ class_Groups_Ogroup__add(X3306)
| c_Groups_Oplus__class_Oplus(X3306,c_Groups_Ominus__class_Ominus(X3306,X3305,X3304),X3304) = X3305 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
fof(i_0_2206,plain,
! [X4655,X4656] :
( ( X4656 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4656),X4655) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4656) )
& ( X4655 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4656),X4655) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4656) )
& ( X4656 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X4655 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4656),X4655) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4656) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
cnf(i_0_2207,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_1349]) ).
fof(i_0_2208,plain,
! [X2930,X2931,X2932] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2932,X2931) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2930,X2931)
| X2932 = X2930 )
& ( X2932 != X2930
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2932,X2931) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2930,X2931) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_2209,plain,
! [X2933,X2934,X2935] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2935,X2934) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2935,X2933)
| X2934 = X2933 )
& ( X2934 != X2933
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2935,X2934) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2935,X2933) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
cnf(i_0_2210,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_1430]) ).
cnf(i_0_2211,plain,
c_Int_Osucc(c_Int_Opred(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_1431]) ).
cnf(i_0_2212,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1370]) ).
cnf(i_0_2213,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_1432]) ).
fof(i_0_2214,plain,
! [X2956,X2957,X2959,X2960,X2961] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2957,X2956)
| X2956 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2957,esk4_2(X2956,X2957)) )
& ( X2959 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2960,X2961)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2960,X2959) ) ),
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_2215,plain,
! [X2829,X2830,X2832,X2833,X2834] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2830,X2829)
| X2829 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2830,esk2_2(X2829,X2830)) )
& ( X2832 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2833,X2834)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2833,X2832) ) ),
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_2216,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1433]) ).
fof(i_0_2217,plain,
! [X4292,X4293] :
( ~ class_Rings_Olinordered__semidom(X4293)
| ~ c_Orderings_Oord__class_Oless(X4293,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4293),X4292),c_Groups_Ozero__class_Ozero(X4293)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1434])]) ).
fof(i_0_2218,plain,
! [X3078,X3079] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3079,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3079,X3078)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(i_0_2219,plain,
! [X3413,X3414] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3414,X3413),X3414) = X3413,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
fof(i_0_2220,plain,
! [X3411,X3412] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3412,X3411),X3411) = X3412,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).
fof(i_0_2221,plain,
! [X5315,X5316] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5316,X5315),X5316),
inference(variable_rename,[status(thm)],[fact_div__le__dividend]) ).
fof(i_0_2222,plain,
! [X3441,X3442] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3442,X3441),X3442),
inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).
fof(i_0_2223,plain,
! [X2835,X2836] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2836,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2836,X2835)),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_2224,plain,
! [X2837,X2838] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2838,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2837,X2838)),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_2225,plain,
! [X3909] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X3909))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3909) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3909)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X3909)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])]) ).
fof(i_0_2226,plain,
! [X3805] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3805),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3805,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3805,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3805),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one])]) ).
fof(i_0_2227,plain,
! [X3762,X3763] :
( ( ~ c_Orderings_Oord__class_Oless(X3763,c_Groups_Ozero__class_Ozero(X3763),c_Groups_Oabs__class_Oabs(X3763,X3762))
| X3762 != c_Groups_Ozero__class_Ozero(X3763)
| ~ class_Groups_Oordered__ab__group__add__abs(X3763) )
& ( X3762 = c_Groups_Ozero__class_Ozero(X3763)
| c_Orderings_Oord__class_Oless(X3763,c_Groups_Ozero__class_Ozero(X3763),c_Groups_Oabs__class_Oabs(X3763,X3762))
| ~ class_Groups_Oordered__ab__group__add__abs(X3763) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).
cnf(i_0_2228,plain,
( X1 = c_Nat_OSuc(esk23_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_1435]) ).
fof(i_0_2229,plain,
! [X4942] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),esk66_1(X4942))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4942) )
& ( X4942 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk66_1(X4942))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4942) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__imp__eq__int])])])]) ).
fof(i_0_2230,plain,
! [X4690,X4691,X4692] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4691),X4692) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4690),X4692)
| X4691 = X4690
| X4692 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4691 != X4690
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4691),X4692) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4690),X4692)
| X4692 = 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_2231,plain,
! [X4703,X4704,X4705] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4705),X4704) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4703),X4704)
| X4705 = X4703
| X4704 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4705 != X4703
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4705),X4704) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4703),X4704) )
& ( X4704 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4705),X4704) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4703),X4704) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_2232,plain,
! [X4693,X4694,X4695] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4695),X4694) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4695),X4693)
| X4694 = X4693
| X4695 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4694 != X4693
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4695),X4694) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4695),X4693)
| X4695 = 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_2233,plain,
! [X4873,X4874,X4875] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4875),X4874) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4875),X4873)
| X4875 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4874 = X4873 )
& ( X4875 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4875),X4874) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4875),X4873) )
& ( X4874 != X4873
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4875),X4874) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4875),X4873) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_2234,plain,
! [X4700,X4701,X4702] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4702),X4701) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4702),X4700)
| X4701 = X4700
| X4702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4701 != X4700
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4702),X4701) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4702),X4700) )
& ( X4702 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4702),X4701) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4702),X4700) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_2235,plain,
! [X4033,X4034] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4034,X4033)
| c_Nat__Transfer_Otsub(X4033,X4034) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4033,X4034) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).
fof(i_0_2236,plain,
! [X4011,X4012] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4012,X4011)
| c_Nat__Transfer_Otsub(X4011,X4012) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4011,X4012) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4012,X4011)
| c_Nat__Transfer_Otsub(X4011,X4012) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1436])]) ).
fof(i_0_2237,plain,
! [X3358,X3359,X3360] :
( ~ class_Orderings_Oorder(X3360)
| ~ c_Orderings_Oord__class_Oless__eq(X3360,X3359,X3358)
| X3358 = X3359
| c_Orderings_Oord__class_Oless(X3360,X3359,X3358) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_2238,plain,
! [X3355,X3356,X3357] :
( ~ class_Orderings_Oorder(X3357)
| ~ c_Orderings_Oord__class_Oless__eq(X3357,X3356,X3355)
| X3356 = X3355
| c_Orderings_Oord__class_Oless(X3357,X3356,X3355) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_2239,plain,
! [X3352,X3353,X3354] :
( ~ class_Orderings_Oorder(X3354)
| ~ c_Orderings_Oord__class_Oless__eq(X3354,X3353,X3352)
| c_Orderings_Oord__class_Oless(X3354,X3353,X3352)
| X3353 = X3352 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_2240,plain,
! [X3337,X3338,X3339] :
( ~ class_Orderings_Oorder(X3339)
| X3338 = X3337
| ~ c_Orderings_Oord__class_Oless__eq(X3339,X3338,X3337)
| c_Orderings_Oord__class_Oless(X3339,X3338,X3337) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_2241,plain,
! [X3325,X3326,X3327] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3327,X3326,X3325)
| c_Orderings_Oord__class_Oless(X3327,X3326,X3325)
| X3326 = X3325
| ~ class_Orderings_Oorder(X3327) )
& ( ~ c_Orderings_Oord__class_Oless(X3327,X3326,X3325)
| c_Orderings_Oord__class_Oless__eq(X3327,X3326,X3325)
| ~ class_Orderings_Oorder(X3327) )
& ( X3326 != X3325
| c_Orderings_Oord__class_Oless__eq(X3327,X3326,X3325)
| ~ class_Orderings_Oorder(X3327) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_2242,plain,
! [X3319,X3320,X3321] :
( ( c_Orderings_Oord__class_Oless__eq(X3321,X3320,X3319)
| ~ c_Orderings_Oord__class_Oless(X3321,X3320,X3319)
| ~ class_Orderings_Oorder(X3321) )
& ( X3320 != X3319
| ~ c_Orderings_Oord__class_Oless(X3321,X3320,X3319)
| ~ class_Orderings_Oorder(X3321) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3321,X3320,X3319)
| X3320 = X3319
| c_Orderings_Oord__class_Oless(X3321,X3320,X3319)
| ~ class_Orderings_Oorder(X3321) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_2243,plain,
! [X3334,X3335,X3336] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3336,X3335,X3334)
| X3335 = X3334
| c_Orderings_Oord__class_Oless(X3336,X3335,X3334)
| ~ class_Orderings_Olinorder(X3336) )
& ( X3335 != X3334
| c_Orderings_Oord__class_Oless__eq(X3336,X3335,X3334)
| c_Orderings_Oord__class_Oless(X3336,X3335,X3334)
| ~ class_Orderings_Olinorder(X3336) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1437])])]) ).
fof(i_0_2244,plain,
! [X3340,X3341,X3342] :
( ~ class_Orderings_Oorder(X3342)
| X3341 = X3340
| ~ c_Orderings_Oord__class_Oless__eq(X3342,X3340,X3341)
| c_Orderings_Oord__class_Oless(X3342,X3340,X3341) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_2245,plain,
! [X3881,X3882] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3882,X3881)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X3882),c_RComplete_Onatfloor(X3881)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__mono])]) ).
fof(i_0_2246,plain,
! [X3751,X3752] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3752,X3751)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3752),c_RComplete_Onatceiling(X3751)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__mono])]) ).
fof(i_0_2247,plain,
! [X3756,X3757] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3757,c_Groups_Oabs__class_Oabs(X3757,X3756),c_Groups_Ozero__class_Ozero(X3757))
| X3756 = c_Groups_Ozero__class_Ozero(X3757)
| ~ class_Groups_Oordered__ab__group__add__abs(X3757) )
& ( X3756 != c_Groups_Ozero__class_Ozero(X3757)
| c_Orderings_Oord__class_Oless__eq(X3757,c_Groups_Oabs__class_Oabs(X3757,X3756),c_Groups_Ozero__class_Ozero(X3757))
| ~ class_Groups_Oordered__ab__group__add__abs(X3757) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).
fof(i_0_2248,plain,
! [X3346,X3347,X3348] :
( ~ class_Orderings_Opreorder(X3348)
| ~ c_Orderings_Oord__class_Oless(X3348,X3347,X3346)
| c_Orderings_Oord__class_Oless__eq(X3348,X3347,X3346) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
cnf(i_0_2249,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_1435]) ).
fof(i_0_2250,plain,
! [X3821] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3821)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3821) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3821)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3821) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).
fof(i_0_2251,plain,
! [X3959,X3960] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3960,X3959))
| X3959 != c_Groups_Ozero__class_Ozero(X3960)
| ~ class_RealVector_Oreal__normed__vector(X3960) )
& ( X3959 = c_Groups_Ozero__class_Ozero(X3960)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3960,X3959))
| ~ class_RealVector_Oreal__normed__vector(X3960) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).
fof(i_0_2252,plain,
! [X3760,X3761] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3761)
| ~ c_Orderings_Oord__class_Oless(X3761,c_Groups_Oabs__class_Oabs(X3761,X3760),c_Groups_Ozero__class_Ozero(X3761)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1438])]) ).
fof(i_0_2253,plain,
! [X4744] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4744,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4744),X4744)),
inference(variable_rename,[status(thm)],[fact_le__square]) ).
fof(i_0_2254,plain,
! [X4595] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4595),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X4595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4595 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4595),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__le__0__conv])]) ).
fof(i_0_2255,plain,
! [X3681] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3681),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X3681 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3681 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3681),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_2256,plain,
! [X3957,X3958] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3958,X3957),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X3957 = c_Groups_Ozero__class_Ozero(X3958)
| ~ class_RealVector_Oreal__normed__vector(X3958) )
& ( X3957 != c_Groups_Ozero__class_Ozero(X3958)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3958,X3957),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X3958) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])]) ).
fof(i_0_2257,plain,
! [X3080,X3081] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3081,X3080) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3081,X3080) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3081,X3080)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3081,X3080) = 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_2258,plain,
! [X3848,X3849] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3849,X3848)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3849,X3848) )
& ( X3849 != X3848
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3849,X3848) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3849,X3848)
| X3849 = X3848
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3849,X3848) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
fof(i_0_2259,plain,
! [X3468,X3469] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3469,X3468)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3469,X3468)
| X3469 = X3468 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3469,X3468)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3469,X3468) )
& ( X3469 != X3468
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3469,X3468) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(i_0_2260,plain,
! [X3466,X3467] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3467,X3466)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3467,X3466) )
& ( X3467 != X3466
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3467,X3466) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3467,X3466)
| X3467 = X3466
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3467,X3466) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
fof(i_0_2261,plain,
! [X3513,X3514] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3514,X3513)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3514,X3513) )
& ( X3514 != X3513
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3514,X3513) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3514,X3513)
| X3514 = X3513
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3514,X3513) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_2262,plain,
! [X3511,X3512] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3512,X3511)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3512,X3511)
| X3512 = X3511 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3512,X3511)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3512,X3511) )
& ( X3512 != X3511
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3512,X3511) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_2263,plain,
! [X3507,X3508] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3508,X3507)
| X3508 = X3507
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3508,X3507) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_2264,plain,
! [X5312,X5313] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5313,X5312)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5313,X5312) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])]) ).
fof(i_0_2265,plain,
! [X3082,X3083] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3083,X3082)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3083,X3082) = 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_2266,plain,
! [X4444] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4444),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[i_0_1439]) ).
fof(i_0_2267,plain,
! [X3675] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3675),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[i_0_1440]) ).
fof(i_0_2268,plain,
! [X3509,X3510] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3510,X3509)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3510,X3509) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_2269,plain,
! [X3505,X3506] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3506,X3505)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3506,X3505) )
& ( X3506 != X3505
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3506,X3505) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_2270,plain,
! [X3503,X3504] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3504,X3503)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3504,X3503) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_2271,plain,
! [X3952,X3953] :
( ~ class_RealVector_Oreal__normed__vector(X3953)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3953,X3952),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1441])]) ).
cnf(i_0_2272,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__Suc0__eq__1]) ).
cnf(i_0_2273,plain,
hAPP(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_2274,plain,
! [X4999,X5000] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4999) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5000),c_Groups_Ozero__class_Ozero(X5000)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4999)) = c_Groups_Oone__class_Oone(X5000)
| ~ class_Power_Opower(X5000)
| ~ class_Rings_Osemiring__0(X5000) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4999) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5000),c_Groups_Ozero__class_Ozero(X5000)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4999)) = c_Groups_Ozero__class_Ozero(X5000)
| ~ class_Power_Opower(X5000)
| ~ class_Rings_Osemiring__0(X5000) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left__number__of])])]) ).
fof(i_0_2275,plain,
! [X3834] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X3834),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X3834 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X3834 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X3834),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff])]) ).
fof(i_0_2276,plain,
! [X2741,X2742] :
( hAPP(X2742,esk1_2(X2741,X2742)) != hAPP(X2741,esk1_2(X2741,X2742))
| X2742 = X2741 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
cnf(i_0_2277,plain,
( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1408]) ).
fof(i_0_2278,plain,
! [X5097,X5098,X5099] :
( ( X5098 = c_Groups_Ozero__class_Ozero(X5099)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5099),X5098),X5097) != c_Groups_Ozero__class_Ozero(X5099)
| ~ class_Power_Opower(X5099)
| ~ class_Rings_Omult__zero(X5099)
| ~ class_Rings_Ono__zero__divisors(X5099)
| ~ class_Rings_Ozero__neq__one(X5099) )
& ( X5097 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5099),X5098),X5097) != c_Groups_Ozero__class_Ozero(X5099)
| ~ class_Power_Opower(X5099)
| ~ class_Rings_Omult__zero(X5099)
| ~ class_Rings_Ono__zero__divisors(X5099)
| ~ class_Rings_Ozero__neq__one(X5099) )
& ( X5098 != c_Groups_Ozero__class_Ozero(X5099)
| X5097 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5099),X5098),X5097) = c_Groups_Ozero__class_Ozero(X5099)
| ~ class_Power_Opower(X5099)
| ~ class_Rings_Omult__zero(X5099)
| ~ class_Rings_Ono__zero__divisors(X5099)
| ~ class_Rings_Ozero__neq__one(X5099) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_2279,plain,
! [X3102,X3103,X3104] :
( ( X3103 = X3102
| c_Orderings_Oord__class_Oless(X3104,X3103,X3102)
| c_Orderings_Oord__class_Oless(X3104,X3102,X3103)
| ~ class_Orderings_Olinorder(X3104) )
& ( ~ c_Orderings_Oord__class_Oless(X3104,X3103,X3102)
| X3103 != X3102
| ~ class_Orderings_Olinorder(X3104) )
& ( ~ c_Orderings_Oord__class_Oless(X3104,X3102,X3103)
| X3103 != X3102
| ~ class_Orderings_Olinorder(X3104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_2280,plain,
! [X3678,X3679,X3680] :
( ~ class_Rings_Olinordered__idom(X3680)
| X3679 = X3678
| c_Orderings_Oord__class_Oless(X3680,X3679,X3678)
| c_Orderings_Oord__class_Oless(X3680,X3678,X3679) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1442])]) ).
fof(i_0_2281,plain,
! [X3225,X3226,X3227] :
( ~ class_Orderings_Olinorder(X3227)
| c_Orderings_Oord__class_Oless(X3227,X3226,X3225)
| X3226 = X3225
| c_Orderings_Oord__class_Oless(X3227,X3225,X3226) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1443])]) ).
fof(i_0_2282,plain,
! [X3141,X3142,X3143] :
( ~ class_Orderings_Olinorder(X3143)
| X3142 = X3141
| c_Orderings_Oord__class_Oless(X3143,X3142,X3141)
| c_Orderings_Oord__class_Oless(X3143,X3141,X3142) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1444])]) ).
fof(i_0_2283,plain,
! [X3138,X3139,X3140] :
( ( c_Orderings_Oord__class_Oless(X3140,X3138,X3139)
| X3138 = X3139
| c_Orderings_Oord__class_Oless(X3140,X3139,X3138)
| ~ class_Orderings_Olinorder(X3140) )
& ( X3138 != X3139
| ~ c_Orderings_Oord__class_Oless(X3140,X3138,X3139)
| c_Orderings_Oord__class_Oless(X3140,X3139,X3138)
| ~ class_Orderings_Olinorder(X3140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1445])])]) ).
fof(i_0_2284,plain,
! [X3126,X3127,X3128] :
( ~ class_Orderings_Olinorder(X3128)
| c_Orderings_Oord__class_Oless(X3128,X3127,X3126)
| X3127 = X3126
| c_Orderings_Oord__class_Oless(X3128,X3126,X3127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_2285,plain,
! [X3764,X3765] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3765)
| ~ c_Orderings_Oord__class_Oless(X3765,c_Groups_Ozero__class_Ozero(X3765),X3764)
| c_Groups_Oabs__class_Oabs(X3765,X3764) = X3764 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).
fof(i_0_2286,plain,
! [X3758,X3759] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3759)
| ~ c_Orderings_Oord__class_Oless__eq(X3759,c_Groups_Ozero__class_Ozero(X3759),X3758)
| c_Groups_Oabs__class_Oabs(X3759,X3758) = X3758 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
fof(i_0_2287,plain,
! [X3331,X3332,X3333] :
( ~ class_Orderings_Olinorder(X3333)
| c_Orderings_Oord__class_Oless__eq(X3333,X3332,X3331)
| c_Orderings_Oord__class_Oless(X3333,X3331,X3332) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1446])]) ).
fof(i_0_2288,plain,
! [X3316,X3317,X3318] :
( ~ class_Orderings_Olinorder(X3318)
| c_Orderings_Oord__class_Oless__eq(X3318,X3317,X3316)
| c_Orderings_Oord__class_Oless(X3318,X3316,X3317) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_2289,plain,
! [X3328,X3329,X3330] :
( ~ class_Orderings_Olinorder(X3330)
| c_Orderings_Oord__class_Oless(X3330,X3329,X3328)
| c_Orderings_Oord__class_Oless__eq(X3330,X3328,X3329) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1447])]) ).
fof(i_0_2290,plain,
! [X2891,X2892,X2893] :
( ~ class_Orderings_Olinorder(X2893)
| c_Orderings_Oord__class_Oless__eq(X2893,X2892,X2891)
| c_Orderings_Oord__class_Oless__eq(X2893,X2891,X2892) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_2291,plain,
! [X2839,X2840,X2841] :
( ~ class_Orderings_Olinorder(X2841)
| c_Orderings_Oord__class_Oless__eq(X2841,X2840,X2839)
| c_Orderings_Oord__class_Oless__eq(X2841,X2839,X2840) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1448])]) ).
fof(i_0_2292,plain,
! [X3009,X3010,X3011] :
( ~ class_Rings_Ocomm__semiring__1(X3011)
| c_Groups_Oplus__class_Oplus(X3011,X3010,X3009) = c_Groups_Oplus__class_Oplus(X3011,X3009,X3010) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_2293,plain,
! [X3657] :
( ~ class_Rings_Olinordered__semidom(X3657)
| ~ c_Orderings_Oord__class_Oless(X3657,c_Groups_Oone__class_Oone(X3657),c_Groups_Ozero__class_Ozero(X3657)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1449])]) ).
fof(i_0_2294,plain,
! [X3660] :
( ~ class_Rings_Olinordered__semidom(X3660)
| ~ c_Orderings_Oord__class_Oless__eq(X3660,c_Groups_Oone__class_Oone(X3660),c_Groups_Ozero__class_Ozero(X3660)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1450])]) ).
cnf(i_0_2295,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_1451]) ).
fof(i_0_2296,plain,
! [X4230,X4231,X4232] :
( ~ class_Rings_Ocomm__semiring__1(X4232)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4232),X4231),X4230) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4232),X4230),X4231) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
cnf(i_0_2297,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_1407]) ).
fof(i_0_2298,plain,
! [X3837,X3838] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3838,X3837)
| X3838 = X3837
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3837,X3838) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_2299,plain,
! [X3144,X3145] :
( X3145 = X3144
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3145,X3144)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3144,X3145) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1452])]) ).
fof(i_0_2300,plain,
! [X3100,X3101] :
( ( X3101 = X3100
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3101,X3100)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3100,X3101) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3101,X3100)
| X3101 != X3100 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3100,X3101)
| X3101 != X3100 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_2301,plain,
! [X3871,X3872] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3872,X3871)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3871,X3872) ),
inference(variable_rename,[status(thm)],[fact_zle__linear]) ).
fof(i_0_2302,plain,
! [X2977,X2978] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2978,X2977)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2977,X2978) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(i_0_2303,plain,
! [X2782,X2783] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2783,X2782)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2782,X2783) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_2304,plain,
! [X4112,X4113,X4114] :
( ~ class_Rings_Ono__zero__divisors(X4114)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4114),X4113),X4112) != c_Groups_Ozero__class_Ozero(X4114)
| X4113 = c_Groups_Ozero__class_Ozero(X4114)
| X4112 = c_Groups_Ozero__class_Ozero(X4114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_2305,plain,
! [X4109,X4110,X4111] :
( ~ class_Rings_Ono__zero__divisors(X4111)
| X4110 = c_Groups_Ozero__class_Ozero(X4111)
| X4109 = c_Groups_Ozero__class_Ozero(X4111)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4111),X4110),X4109) != c_Groups_Ozero__class_Ozero(X4111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_2306,plain,
! [X4106,X4107,X4108] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4108),X4107),X4106) != c_Groups_Ozero__class_Ozero(X4108)
| X4107 = c_Groups_Ozero__class_Ozero(X4108)
| X4106 = c_Groups_Ozero__class_Ozero(X4108)
| ~ class_Rings_Oring__no__zero__divisors(X4108) )
& ( X4107 != c_Groups_Ozero__class_Ozero(X4108)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4108),X4107),X4106) = c_Groups_Ozero__class_Ozero(X4108)
| ~ class_Rings_Oring__no__zero__divisors(X4108) )
& ( X4106 != c_Groups_Ozero__class_Ozero(X4108)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4108),X4107),X4106) = c_Groups_Ozero__class_Ozero(X4108)
| ~ class_Rings_Oring__no__zero__divisors(X4108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_2307,plain,
! [X4290,X4291] :
( ~ class_Rings_Olinordered__semidom(X4291)
| c_Orderings_Oord__class_Oless__eq(X4291,c_Groups_Ozero__class_Ozero(X4291),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4291),X4290)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat])]) ).
fof(i_0_2308,plain,
! [X4288,X4289] :
( ~ class_Rings_Olinordered__semidom(X4289)
| c_Orderings_Oord__class_Oless__eq(X4289,c_Groups_Ozero__class_Ozero(X4289),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4289),X4288)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff])]) ).
fof(i_0_2309,plain,
! [X3873,X3874] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3874,X3873) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3873,X3874),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_2310,plain,
! [X2942,X2943] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2943,X2942) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2942,X2943),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_2311,plain,
! [X3684,X3685] :
( ( c_Groups_Oplus__class_Oplus(X3685,X3684,X3684) != c_Groups_Ozero__class_Ozero(X3685)
| X3684 = c_Groups_Ozero__class_Ozero(X3685)
| ~ class_Groups_Olinordered__ab__group__add(X3685) )
& ( X3684 != c_Groups_Ozero__class_Ozero(X3685)
| c_Groups_Oplus__class_Oplus(X3685,X3684,X3684) = c_Groups_Ozero__class_Ozero(X3685)
| ~ class_Groups_Olinordered__ab__group__add(X3685) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_2312,plain,
! [X3519,X3520] :
( ( c_Groups_Ozero__class_Ozero(X3520) != c_Groups_Oplus__class_Oplus(X3520,X3519,X3519)
| X3519 = c_Groups_Ozero__class_Ozero(X3520)
| ~ class_Groups_Olinordered__ab__group__add(X3520) )
& ( X3519 != c_Groups_Ozero__class_Ozero(X3520)
| c_Groups_Ozero__class_Ozero(X3520) = c_Groups_Oplus__class_Oplus(X3520,X3519,X3519)
| ~ class_Groups_Olinordered__ab__group__add(X3520) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_2313,plain,
! [X3120,X3121,X3122] :
( ( X3121 != X3120
| c_Groups_Ominus__class_Ominus(X3122,X3121,X3120) = c_Groups_Ozero__class_Ozero(X3122)
| ~ class_Groups_Oab__group__add(X3122) )
& ( c_Groups_Ominus__class_Ominus(X3122,X3121,X3120) != c_Groups_Ozero__class_Ozero(X3122)
| X3121 = X3120
| ~ class_Groups_Oab__group__add(X3122) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).
fof(i_0_2314,plain,
! [X3129,X3130,X3131] :
( ( c_Groups_Ominus__class_Ominus(X3131,X3130,X3129) != c_Groups_Ozero__class_Ozero(X3131)
| X3130 = X3129
| ~ class_Groups_Ogroup__add(X3131) )
& ( X3130 != X3129
| c_Groups_Ominus__class_Ominus(X3131,X3130,X3129) = c_Groups_Ozero__class_Ozero(X3131)
| ~ class_Groups_Ogroup__add(X3131) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
fof(i_0_2315,plain,
! [X5056,X5057,X5058] :
( ~ class_Rings_Oring__1__no__zero__divisors(X5058)
| X5057 = c_Groups_Ozero__class_Ozero(X5058)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5058),X5057),X5056) != c_Groups_Ozero__class_Ozero(X5058) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_2316,plain,
! [X3529,X3530,X3531] :
( ( X3530 != c_Groups_Oplus__class_Oplus(X3531,X3530,X3529)
| X3529 = c_Groups_Ozero__class_Ozero(X3531)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3531) )
& ( X3529 != c_Groups_Ozero__class_Ozero(X3531)
| X3530 = c_Groups_Oplus__class_Oplus(X3531,X3530,X3529)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3531) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_2317,plain,
! [X4667,X4668] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4667))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4668),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4667)) = c_Groups_Ozero__class_Ozero(X4668)
| ~ class_Int_Onumber__ring(X4668) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4667))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4668),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4667)) = c_Int_Onumber__class_Onumber__of(X4668,X4667)
| ~ class_Int_Onumber__ring(X4668) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1453])])]) ).
fof(i_0_2318,plain,
! [X3753] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3753,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X3753))),
inference(variable_rename,[status(thm)],[fact_real__natceiling__ge]) ).
fof(i_0_2319,plain,
! [X3170,X3171,X3172] :
( ~ class_Orderings_Oorder(X3172)
| ~ c_Orderings_Oord__class_Oless(X3172,X3171,X3170)
| X3170 != X3171 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_2320,plain,
! [X3167,X3168,X3169] :
( ~ class_Orderings_Oorder(X3169)
| ~ c_Orderings_Oord__class_Oless(X3169,X3168,X3167)
| X3168 != X3167 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_2321,plain,
! [X3158,X3159,X3160] :
( ~ class_Orderings_Oorder(X3160)
| ~ c_Orderings_Oord__class_Oless(X3160,X3159,X3158)
| X3159 != X3158 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_2322,plain,
! [X4055] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4055) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4055,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4055,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4055) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__0])]) ).
fof(i_0_2323,plain,
! [X4054] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4054)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4054,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4054,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4054) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).
fof(i_0_2324,plain,
! [X3984] :
( ( c_Nat__Numeral_Oneg(X3984)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3984) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3984)
| ~ c_Nat__Numeral_Oneg(X3984) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1454])]) ).
fof(i_0_2325,plain,
! [X3883] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3883,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(X3883) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__neg])]) ).
fof(i_0_2326,plain,
! [X3749] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3749,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatceiling(X3749) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__neg])]) ).
fof(i_0_2327,plain,
! [X3099] :
( ( X3099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3099) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3099)
| X3099 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_2328,plain,
! [X3754,X3755] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3755)
| c_Orderings_Oord__class_Oless__eq(X3755,c_Groups_Ozero__class_Ozero(X3755),c_Groups_Oabs__class_Oabs(X3755,X3754)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).
fof(i_0_2329,plain,
! [X3097,X3098] :
( ~ class_Orderings_Opreorder(X3098)
| ~ c_Orderings_Oord__class_Oless(X3098,X3097,X3097) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1455])]) ).
fof(i_0_2330,plain,
! [X3985] :
( ( ~ c_Nat__Numeral_Oneg(X3985)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3985,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3985,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Nat__Numeral_Oneg(X3985) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__def])]) ).
fof(i_0_2331,plain,
! [X3544] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3544,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3544 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3544,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_2332,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1456]) ).
cnf(i_0_2333,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1457]) ).
cnf(i_0_2334,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1458]) ).
cnf(i_0_2335,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1459]) ).
cnf(i_0_2336,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1460]) ).
cnf(i_0_2337,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1461]) ).
fof(i_0_2338,plain,
! [X4236,X4237] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4237),X4236) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4236),X4237),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_2339,plain,
! [X4720,X4721] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4721),X4720) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4720),X4721),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(i_0_2340,plain,
! [X4725,X4726] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4726),X4725) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4725),X4726),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_2341,plain,
! [X3540,X3541] :
( ( X3541 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3541,X3540) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3540 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3541,X3540) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3541 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3540 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3541,X3540) = 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_2342,plain,
! [X3152,X3153] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3153,X3152)
| X3152 != 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_2343,plain,
c_Nat_OSuc(X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1462]) ).
cnf(i_0_2344,plain,
X1 != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1463]) ).
fof(i_0_2345,plain,
! [X3955,X3956] :
( ~ class_Int_Onumber__ring(X3956)
| ~ class_RealVector_Oreal__normed__algebra__1(X3956)
| c_RealVector_Onorm__class_Onorm(X3956,c_Int_Onumber__class_Onumber__of(X3956,X3955)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X3955)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__number__of])]) ).
fof(i_0_2346,plain,
! [X3950,X3951] :
( ~ class_RealVector_Oreal__normed__vector(X3951)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3951,X3950)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).
fof(i_0_2347,plain,
! [X5132,X5133] :
( ( X5132 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5133),c_Groups_Ozero__class_Ozero(X5133)),X5132) = c_Groups_Oone__class_Oone(X5133)
| ~ class_Power_Opower(X5133)
| ~ class_Rings_Osemiring__0(X5133) )
& ( X5132 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5133),c_Groups_Ozero__class_Ozero(X5133)),X5132) = c_Groups_Ozero__class_Ozero(X5133)
| ~ class_Power_Opower(X5133)
| ~ class_Rings_Osemiring__0(X5133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_2348,plain,
! [X3542,X3543] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3543,X3542) != X3543
| X3542 = 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_2349,plain,
! [X3113] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3113,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1464]) ).
fof(i_0_2350,plain,
! [X3095] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3095,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1465]) ).
fof(i_0_2351,plain,
! [X3067] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3067,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1466]) ).
fof(i_0_2352,plain,
! [X4443] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4443)),
inference(variable_rename,[status(thm)],[fact_zero__zle__int]) ).
fof(i_0_2353,plain,
! [X4442] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4442)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).
fof(i_0_2354,plain,
! [X3667] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3667)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__ge__zero]) ).
fof(i_0_2355,plain,
! [X3719,X3720] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3720)
| c_Orderings_Oord__class_Oless__eq(X3720,X3719,c_Groups_Oabs__class_Oabs(X3720,X3719)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).
fof(i_0_2356,plain,
! [X3156,X3157] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3157,X3156)
| X3157 != X3156 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_2357,plain,
! [X3154,X3155] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3155,X3154)
| X3154 != X3155 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_2358,plain,
! [X3819] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(X3819)),v_r),
inference(variable_rename,[status(thm)],[fact_g_I1_J]) ).
fof(i_0_2359,plain,
! [X2946,X2947] :
( ~ c_SEQ_Osubseq(X2947)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2946,hAPP(X2947,X2946)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_seq__suble])]) ).
fof(i_0_2360,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_simplification,[status(thm)],[fact_bin__less__0__simps_I1_J]) ).
fof(i_0_2361,plain,
! [X4666] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4666))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4666)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4666))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4666)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4666) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1467])]) ).
fof(i_0_2362,plain,
! [X3992] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3992))
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3992)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3992))
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3992)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X3992) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1468])]) ).
fof(i_0_2363,plain,
! [X4050,X4051] :
( ~ class_Int_Onumber__ring(X4051)
| c_Groups_Oplus__class_Oplus(X4051,c_Int_Onumber__class_Onumber__of(X4051,c_Int_OPls),X4050) = X4050 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).
fof(i_0_2364,plain,
! [X4052,X4053] :
( ~ class_Int_Onumber__ring(X4053)
| c_Groups_Oplus__class_Oplus(X4053,X4052,c_Int_Onumber__class_Onumber__of(X4053,c_Int_OPls)) = X4052 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).
fof(i_0_2365,plain,
! [X4698,X4699] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4699),X4698) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4698 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4699 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4699),X4698) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4698 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4699),X4698) = 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_2366,plain,
! [X3151] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3151,X3151),
inference(variable_rename,[status(thm)],[i_0_1469]) ).
fof(i_0_2367,plain,
! [X3096] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3096,X3096),
inference(variable_rename,[status(thm)],[i_0_1470]) ).
fof(i_0_2368,plain,
! [X4801,X4802] :
( X4802 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4802),X4801)
| X4801 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4802 = 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_2369,plain,
! [X4763,X4764] :
( ( X4764 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4764),X4763) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4763 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4764),X4763) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4764 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4763 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4764),X4763) = 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_2370,plain,
! [X4760,X4761] :
( ( X4761 = 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),X4761),X4760) )
& ( X4760 = 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),X4761),X4760) )
& ( X4761 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4760 != 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),X4761),X4760) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).
fof(i_0_2371,plain,
! [X4129,X4130] :
( ~ class_Rings_Olinordered__idom(X4130)
| c_Groups_Oabs__class_Oabs(X4130,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4130),X4129)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4130),X4129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nat])]) ).
fof(i_0_2372,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(fof_simplification,[status(thm)],[fact_rel__simps_I2_J]) ).
fof(i_0_2373,plain,
! [X5192] :
( ~ class_Power_Opower(X5192)
| c_Power_Opower__class_Opower(X5192) = c_Power_Opower_Opower(X5192,c_Groups_Oone__class_Oone(X5192),c_Groups_Otimes__class_Otimes(X5192)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).
fof(i_0_2374,plain,
! [X4247,X4248] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4248)
| c_RealVector_Onorm__class_Onorm(X4248,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4248),X4247)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X4247) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__nat])]) ).
fof(i_0_2375,plain,
! [X5066,X5067] :
( ~ class_Groups_Omonoid__mult(X5067)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5067),c_Groups_Oone__class_Oone(X5067)),X5066) = c_Groups_Oone__class_Oone(X5067) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_2376,plain,
! [X4102,X4103] :
( ~ class_Rings_Omult__zero(X4103)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4103),c_Groups_Ozero__class_Ozero(X4103)),X4102) = c_Groups_Ozero__class_Ozero(X4103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_2377,plain,
! [X4096,X4097] :
( ~ class_RealVector_Oreal__normed__algebra(X4097)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4097),c_Groups_Ozero__class_Ozero(X4097)),X4096) = c_Groups_Ozero__class_Ozero(X4097) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).
fof(i_0_2378,plain,
! [X4094,X4095] :
( ~ class_RealVector_Oreal__normed__algebra(X4095)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4095),c_Groups_Ozero__class_Ozero(X4095)),X4094) = c_Groups_Ozero__class_Ozero(X4095) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).
fof(i_0_2379,plain,
! [X4098,X4099] :
( ~ class_Rings_Ocomm__semiring__1(X4099)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4099),c_Groups_Ozero__class_Ozero(X4099)),X4098) = c_Groups_Ozero__class_Ozero(X4099) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(i_0_2380,plain,
! [X3658] :
( ~ class_Rings_Olinordered__semidom(X3658)
| c_Orderings_Oord__class_Oless(X3658,c_Groups_Ozero__class_Ozero(X3658),c_Groups_Oone__class_Oone(X3658)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_2381,plain,
! [X3659] :
( ~ class_Rings_Olinordered__semidom(X3659)
| c_Orderings_Oord__class_Oless__eq(X3659,c_Groups_Ozero__class_Ozero(X3659),c_Groups_Oone__class_Oone(X3659)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_2382,plain,
! [X4193,X4194,X4195] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4195),X4194) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4195),X4193)
| X4194 = X4193
| ~ class_Nat_Osemiring__char__0(X4195) )
& ( X4194 != X4193
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4195),X4194) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4195),X4193)
| ~ class_Nat_Osemiring__char__0(X4195) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff])])]) ).
fof(i_0_2383,plain,
! [X4277,X4278] :
( ~ class_Groups_Ocomm__monoid__mult(X4278)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4278),c_Groups_Oone__class_Oone(X4278)),X4277) = X4277 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_2384,plain,
! [X4275,X4276] :
( ~ class_Groups_Omonoid__mult(X4276)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4276),c_Groups_Oone__class_Oone(X4276)),X4275) = X4275 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_2385,plain,
! [X4285,X4286] :
( ~ class_Rings_Ocomm__semiring__1(X4286)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4286),c_Groups_Oone__class_Oone(X4286)),X4285) = X4285 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
fof(i_0_2386,plain,
! [X5278,X5279] :
( ~ class_Divides_Osemiring__div(X5279)
| c_Divides_Odiv__class_Odiv(X5279,c_Groups_Ozero__class_Ozero(X5279),X5278) = c_Groups_Ozero__class_Ozero(X5279) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])]) ).
fof(i_0_2387,plain,
! [X5280,X5281] :
( ~ class_Divides_Osemiring__div(X5281)
| c_Divides_Odiv__class_Odiv(X5281,X5280,c_Groups_Ozero__class_Ozero(X5281)) = c_Groups_Ozero__class_Ozero(X5281) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])]) ).
fof(i_0_2388,plain,
! [X5275,X5276] :
( ~ class_Divides_Osemiring__div(X5276)
| X5275 = c_Groups_Ozero__class_Ozero(X5276)
| c_Divides_Odiv__class_Odiv(X5276,X5275,X5275) = c_Groups_Oone__class_Oone(X5276) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).
fof(i_0_2389,plain,
! [X4104,X4105] :
( ~ class_Rings_Omult__zero(X4105)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4105),X4104),c_Groups_Ozero__class_Ozero(X4105)) = c_Groups_Ozero__class_Ozero(X4105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_2390,plain,
! [X4092,X4093] :
( ~ class_RealVector_Oreal__normed__algebra(X4093)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4093),X4092),c_Groups_Ozero__class_Ozero(X4093)) = c_Groups_Ozero__class_Ozero(X4093) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
fof(i_0_2391,plain,
! [X4090,X4091] :
( ~ class_RealVector_Oreal__normed__algebra(X4091)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4091),X4090),c_Groups_Ozero__class_Ozero(X4091)) = c_Groups_Ozero__class_Ozero(X4091) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).
fof(i_0_2392,plain,
! [X4100,X4101] :
( ~ class_Rings_Ocomm__semiring__1(X4101)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4101),X4100),c_Groups_Ozero__class_Ozero(X4101)) = c_Groups_Ozero__class_Ozero(X4101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(i_0_2393,plain,
! [X3517,X3518] :
( ~ class_Groups_Ocomm__monoid__add(X3518)
| c_Groups_Oplus__class_Oplus(X3518,c_Groups_Ozero__class_Ozero(X3518),X3517) = X3517 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_2394,plain,
! [X3515,X3516] :
( ~ class_Groups_Omonoid__add(X3516)
| c_Groups_Oplus__class_Oplus(X3516,c_Groups_Ozero__class_Ozero(X3516),X3515) = X3515 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_2395,plain,
! [X3525,X3526] :
( ~ class_Rings_Ocomm__semiring__1(X3526)
| c_Groups_Oplus__class_Oplus(X3526,c_Groups_Ozero__class_Ozero(X3526),X3525) = X3525 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_2396,plain,
! [X5290,X5291] :
( ~ class_Divides_Osemiring__div(X5291)
| c_Divides_Odiv__class_Odiv(X5291,X5290,c_Groups_Oone__class_Oone(X5291)) = X5290 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).
fof(i_0_2397,plain,
! [X3114,X3115] :
( ~ class_Groups_Ogroup__add(X3115)
| c_Groups_Ominus__class_Ominus(X3115,X3114,c_Groups_Ozero__class_Ozero(X3115)) = X3114 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).
fof(i_0_2398,plain,
! [X3523,X3524] :
( ~ class_Groups_Ocomm__monoid__add(X3524)
| c_Groups_Oplus__class_Oplus(X3524,X3523,c_Groups_Ozero__class_Ozero(X3524)) = X3523 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_2399,plain,
! [X3521,X3522] :
( ~ class_Groups_Omonoid__add(X3522)
| c_Groups_Oplus__class_Oplus(X3522,X3521,c_Groups_Ozero__class_Ozero(X3522)) = X3521 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_2400,plain,
! [X3527,X3528] :
( ~ class_Rings_Ocomm__semiring__1(X3528)
| c_Groups_Oplus__class_Oplus(X3528,X3527,c_Groups_Ozero__class_Ozero(X3528)) = X3527 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_2401,plain,
! [X5108,X5109] :
( ~ class_Power_Opower(X5109)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5109),X5108),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_2402,plain,
! [X4960,X4961] :
( ~ class_Rings_Ocomm__semiring__1(X4961)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4961),X4960),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4961) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
fof(i_0_2403,plain,
! [X4281,X4282] :
( ~ class_Groups_Ocomm__monoid__mult(X4282)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4282),X4281),c_Groups_Oone__class_Oone(X4282)) = X4281 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_2404,plain,
! [X4279,X4280] :
( ~ class_Groups_Omonoid__mult(X4280)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4280),X4279),c_Groups_Oone__class_Oone(X4280)) = X4279 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_2405,plain,
! [X4283,X4284] :
( ~ class_Rings_Ocomm__semiring__1(X4284)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4284),X4283),c_Groups_Oone__class_Oone(X4284)) = X4283 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(i_0_2406,plain,
! [X3117,X3118] :
( ~ class_Groups_Ogroup__add(X3118)
| c_Groups_Ominus__class_Ominus(X3118,X3117,X3117) = c_Groups_Ozero__class_Ozero(X3118) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(i_0_2407,plain,
! [X2885,X2886,X2887] :
( ~ class_Orderings_Opreorder(X2887)
| X2886 != X2885
| c_Orderings_Oord__class_Oless__eq(X2887,X2886,X2885) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_2408,plain,
! [X5078,X5079] :
( ~ class_Groups_Omonoid__mult(X5079)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5079),X5078),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X5078 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_2409,plain,
! [X4968,X4969] :
( ~ class_Rings_Ocomm__semiring__1(X4969)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4969),X4968),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4968 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).
fof(i_0_2410,plain,
! [X3880] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X3880)),
inference(variable_rename,[status(thm)],[fact_zero__le__natfloor]) ).
fof(i_0_2411,plain,
! [X3750] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X3750)),
inference(variable_rename,[status(thm)],[fact_zero__le__natceiling]) ).
fof(i_0_2412,plain,
! [X2744,X2745] :
( ~ class_Orderings_Opreorder(X2745)
| c_Orderings_Oord__class_Oless__eq(X2745,X2744,X2744) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_2413,plain,
! [X4128] : c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4128)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4128),
inference(variable_rename,[status(thm)],[fact_abs__int__eq]) ).
fof(i_0_2414,plain,
! [X3748] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3748)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3748),
inference(variable_rename,[status(thm)],[fact_abs__real__of__nat__cancel]) ).
cnf(i_0_2415,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_2416,plain,
! [X3727,X3728] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3728)
| c_Groups_Oabs__class_Oabs(X3728,c_Groups_Oabs__class_Oabs(X3728,X3727)) = c_Groups_Oabs__class_Oabs(X3728,X3727) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).
fof(i_0_2417,plain,
! [X3709,X3710,X3711] :
( ( c_Int_Onumber__class_Onumber__of(X3711,X3710) != c_Int_Onumber__class_Onumber__of(X3711,X3709)
| X3710 = X3709
| ~ class_Int_Onumber__ring(X3711)
| ~ class_Int_Oring__char__0(X3711) )
& ( X3710 != X3709
| c_Int_Onumber__class_Onumber__of(X3711,X3710) = c_Int_Onumber__class_Onumber__of(X3711,X3709)
| ~ class_Int_Onumber__ring(X3711)
| ~ class_Int_Oring__char__0(X3711) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).
fof(i_0_2418,plain,
! [X3224] :
( X3224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3224) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_2419,plain,
! [X3945,X3946] :
( ~ class_RealVector_Oreal__normed__vector(X3946)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3946,X3945)) = c_RealVector_Onorm__class_Onorm(X3946,X3945) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])]) ).
fof(i_0_2420,plain,
! [X5274] :
( X5274 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5274,X5274) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).
fof(i_0_2421,plain,
! [X5277] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5277) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zdiv__zero]) ).
fof(i_0_2422,plain,
! [X3108] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3108) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).
fof(i_0_2423,plain,
! [X3986] :
( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3986))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3986) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__number__of__eq__0])]) ).
fof(i_0_2424,plain,
! [X4127] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4127)),
inference(variable_rename,[status(thm)],[i_0_1471]) ).
fof(i_0_2425,plain,
! [X3851] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3851) = X3851,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_2426,plain,
! [X3538] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3538) = X3538,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_2427,plain,
! [X3116] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3116,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(i_0_2428,plain,
! [X3850] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3850,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X3850,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_2429,plain,
! [X3539] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3539,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3539,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_2430,plain,
! [X2784,X2785] :
( X2785 != X2784
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2785,X2784) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_2431,plain,
! [X3545] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3545),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_2432,plain,
! [X3071] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3071),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_2433,plain,
! [X4754,X4755] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4755) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4754)
| X4755 = X4754 )
& ( X4755 != X4754
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4755) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4754) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J])]) ).
fof(i_0_2434,plain,
! [X4727,X4728] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4728) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4727)
| X4728 = X4727 )
& ( X4728 != X4727
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4728) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4727) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__int__eq])]) ).
fof(i_0_2435,plain,
! [X2967,X2968] :
( ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2968) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2967)
| X2968 = X2967 )
& ( X2968 != X2967
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2968) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2967) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject])]) ).
fof(i_0_2436,plain,
! [X3119] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3119,X3119) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).
fof(i_0_2437,plain,
! [X4696] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4696) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_2438,plain,
! [X4274] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X4274) = X4274,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_2439,plain,
! [X4758] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X4758) = X4758,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(i_0_2440,plain,
! [X4759] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4759) = X4759,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_2441,plain,
! [X3875] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3875,X3875),
inference(variable_rename,[status(thm)],[fact_zle__refl]) ).
fof(i_0_2442,plain,
! [X2979] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2979,X2979),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(i_0_2443,plain,
! [X2781] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2781,X2781),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_2444,plain,
! [X4045] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X4045) = X4045,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(i_0_2445,plain,
! [X4047] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4047,c_Int_OPls) = X4047,
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J]) ).
fof(i_0_2446,plain,
! [X4046] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4046,c_Int_OPls) = X4046,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(i_0_2447,plain,
! [X4697] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4697),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_2448,plain,
! [X5336,X5337] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X5337,X5336)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5337),
inference(variable_rename,[status(thm)],[fact_complex__mod__rcis]) ).
fof(i_0_2449,plain,
! [X4273] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4273),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X4273,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_2450,plain,
! [X4762] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4762),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4762,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_2451,plain,
! [X3703,X3704] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3704,X3703) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3703 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3704))
| ~ class_Groups_Ozero(X3704) )
& ( X3703 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3704))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3704,X3703) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X3704) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff])])]) ).
fof(i_0_2452,plain,
! [X3028,X3029] :
( ~ class_Orderings_Oorder(X3029)
| ~ c_SEQ_Oincseq(X3029,X3028)
| c_SEQ_Omonoseq(X3029,X3028) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incseq__imp__monoseq])]) ).
fof(i_0_2453,plain,
! [X3030,X3031] :
( ~ class_Orderings_Oorder(X3031)
| ~ c_SEQ_Odecseq(X3031,X3030)
| c_SEQ_Omonoseq(X3031,X3030) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decseq__imp__monoseq])]) ).
fof(i_0_2454,plain,
! [X4287] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X4287) = c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).
fof(i_0_2455,plain,
! [X3713,X3714] :
( ( c_Groups_Oabs__class_Oabs(X3714,X3713) != c_Groups_Ozero__class_Ozero(X3714)
| X3713 = c_Groups_Ozero__class_Ozero(X3714)
| ~ class_Groups_Oordered__ab__group__add__abs(X3714) )
& ( X3713 != c_Groups_Ozero__class_Ozero(X3714)
| c_Groups_Oabs__class_Oabs(X3714,X3713) = c_Groups_Ozero__class_Ozero(X3714)
| ~ class_Groups_Oordered__ab__group__add__abs(X3714) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).
fof(i_0_2456,plain,
! [X3856] : c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X3856)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3856),
inference(variable_rename,[status(thm)],[fact_natfloor__number__of__eq]) ).
fof(i_0_2457,plain,
! [X3879] : c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X3879)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3879),
inference(variable_rename,[status(thm)],[fact_natceiling__number__of__eq]) ).
fof(i_0_2458,plain,
! [X3947,X3948] :
( ( c_RealVector_Onorm__class_Onorm(X3948,X3947) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3947 = c_Groups_Ozero__class_Ozero(X3948)
| ~ class_RealVector_Oreal__normed__vector(X3948) )
& ( X3947 != c_Groups_Ozero__class_Ozero(X3948)
| c_RealVector_Onorm__class_Onorm(X3948,X3947) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X3948) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).
fof(i_0_2459,plain,
~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
inference(fof_simplification,[status(thm)],[fact_not__neg__number__of__Pls]) ).
fof(i_0_2460,plain,
! [X5388,X5389] :
( ~ class_Orderings_Oorder(X5389)
| class_Orderings_Oorder(tc_fun(X5388,X5389)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_2461,plain,
! [X5390,X5391] :
( ~ class_Orderings_Oord(X5391)
| class_Orderings_Oord(tc_fun(X5390,X5391)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_2462,plain,
! [X5386,X5387] :
( ~ class_Orderings_Opreorder(X5387)
| class_Orderings_Opreorder(tc_fun(X5386,X5387)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_2463,plain,
! [X3876] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3876)) = X3876,
inference(variable_rename,[status(thm)],[fact_natfloor__real__of__nat]) ).
fof(i_0_2464,plain,
! [X3712] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3712)) = X3712,
inference(variable_rename,[status(thm)],[fact_natceiling__real__of__nat]) ).
fof(i_0_2465,plain,
! [X4311] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4311) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4311 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4311 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4311) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv])]) ).
fof(i_0_2466,plain,
! [X3674] :
( ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3674) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3674 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3674) = 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_2467,plain,
! [X4294] :
( ~ class_Rings_Osemiring__1(X4294)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4294),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X4294) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0])]) ).
fof(i_0_2468,plain,
! [X4310] :
( ~ class_Rings_Osemiring__1(X4310)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4310),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4310) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__1])]) ).
fof(i_0_2469,plain,
! [X3715] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3715)
| c_Groups_Oabs__class_Oabs(X3715,c_Groups_Ozero__class_Ozero(X3715)) = c_Groups_Ozero__class_Ozero(X3715) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).
fof(i_0_2470,plain,
! [X3705] :
( ~ class_Rings_Olinordered__idom(X3705)
| c_Groups_Oabs__class_Oabs(X3705,c_Groups_Oone__class_Oone(X3705)) = c_Groups_Oone__class_Oone(X3705) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).
fof(i_0_2471,plain,
! [X3949] :
( ~ class_RealVector_Oreal__normed__vector(X3949)
| c_RealVector_Onorm__class_Onorm(X3949,c_Groups_Ozero__class_Ozero(X3949)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__zero])]) ).
fof(i_0_2472,plain,
! [X3954] :
( ~ class_RealVector_Oreal__normed__algebra__1(X3954)
| c_RealVector_Onorm__class_Onorm(X3954,c_Groups_Oone__class_Oone(X3954)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__one])]) ).
fof(i_0_2473,plain,
! [X3941] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3941) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3941),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(i_0_2474,plain,
! [X4048] :
( ~ class_Int_Onumber__ring(X4048)
| c_Int_Onumber__class_Onumber__of(X4048,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X4048) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).
fof(i_0_2475,plain,
! [X4049] :
( ~ class_Int_Onumber__ring(X4049)
| c_Groups_Ozero__class_Ozero(X4049) = c_Int_Onumber__class_Onumber__of(X4049,c_Int_OPls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).
cnf(i_0_2476,plain,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_cis__zero]) ).
fof(i_0_2477,plain,
! [X3687] :
( ~ class_Rings_Ozero__neq__one(X3687)
| c_Groups_Ozero__class_Ozero(X3687) != c_Groups_Oone__class_Oone(X3687) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_2478,plain,
! [X3686] :
( ~ class_Rings_Ozero__neq__one(X3686)
| c_Groups_Oone__class_Oone(X3686) != c_Groups_Ozero__class_Ozero(X3686) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_2479,plain,
! [X4007] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X4007),
inference(variable_rename,[status(thm)],[fact_complex__i__not__number__of]) ).
fof(i_0_2480,plain,
! [X5338] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5338) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(variable_rename,[status(thm)],[fact_rcis__zero__mod]) ).
fof(i_0_2481,plain,
! [X5385] :
( ~ class_Rings_Ocomm__ring(X5385)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X5385)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring])]) ).
fof(i_0_2482,plain,
! [X5384] :
( ~ class_Rings_Ocomm__semiring__0(X5384)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X5384)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0])]) ).
fof(i_0_2483,plain,
! [X5383] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5383)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X5383)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add])]) ).
fof(i_0_2484,plain,
! [X5382] :
( ~ class_Rings_Oidom(X5382)
| class_Rings_Oidom(tc_Polynomial_Opoly(X5382)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom])]) ).
fof(i_0_2485,plain,
! [X5423] :
( ~ class_Fields_Ofield(X5423)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X5423)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Osemiring__div])]) ).
fof(i_0_2486,plain,
! [X5403] :
( ~ class_Rings_Oidom(X5403)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X5403)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors])]) ).
fof(i_0_2487,plain,
! [X5432] :
( ~ class_Rings_Ocomm__ring__1(X5432)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X5432)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1])]) ).
fof(i_0_2488,plain,
! [X5435] :
( ~ class_Rings_Ocomm__semiring__0(X5435)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X5435)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0])]) ).
fof(i_0_2489,plain,
! [X5444] :
( ~ class_Rings_Ocomm__semiring__1(X5444)
| class_Power_Opower(tc_Polynomial_Opoly(X5444)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower])]) ).
fof(i_0_2490,plain,
! [X5396] :
( ~ class_Rings_Olinordered__idom(X5396)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X5396)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict])]) ).
fof(i_0_2491,plain,
! [X5408] :
( ~ class_Rings_Olinordered__idom(X5408)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X5408)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1])]) ).
fof(i_0_2492,plain,
! [X5417] :
( ~ class_Rings_Olinordered__idom(X5417)
| class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X5417)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring__abs])]) ).
fof(i_0_2493,plain,
! [X5411] :
( ~ class_Rings_Olinordered__idom(X5411)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X5411)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring])]) ).
fof(i_0_2494,plain,
! [X5443] :
( ~ class_Rings_Ocomm__ring__1(X5443)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X5443)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1])]) ).
fof(i_0_2495,plain,
! [X5446] :
( ~ class_Rings_Ocomm__ring(X5446)
| class_Rings_Oring(tc_Polynomial_Opoly(X5446)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring])]) ).
fof(i_0_2496,plain,
! [X5395] :
( ~ class_Rings_Olinordered__idom(X5395)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X5395)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict])]) ).
fof(i_0_2497,plain,
! [X5397] :
( ~ class_Rings_Olinordered__idom(X5397)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X5397)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict])]) ).
fof(i_0_2498,plain,
! [X5407] :
( ~ class_Rings_Olinordered__idom(X5407)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X5407)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring])]) ).
fof(i_0_2499,plain,
! [X5416] :
( ~ class_Rings_Olinordered__idom(X5416)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X5416)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring])]) ).
fof(i_0_2500,plain,
! [X5428] :
( ~ class_Rings_Olinordered__idom(X5428)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X5428)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring])]) ).
fof(i_0_2501,plain,
! [X5404] :
( ~ class_Rings_Olinordered__idom(X5404)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X5404)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring])]) ).
fof(i_0_2502,plain,
! [X5405] :
( ~ class_Rings_Olinordered__idom(X5405)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X5405)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict])]) ).
fof(i_0_2503,plain,
! [X5420] :
( ~ class_Rings_Olinordered__idom(X5420)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X5420)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring])]) ).
fof(i_0_2504,plain,
! [X5414] :
( ~ class_Rings_Ocomm__semiring__1(X5414)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X5414)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult])]) ).
fof(i_0_2505,plain,
! [X5431] :
( ~ class_Rings_Ocomm__semiring__1(X5431)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X5431)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult])]) ).
fof(i_0_2506,plain,
! [X5425] :
( ~ class_Rings_Olinordered__idom(X5425)
| class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X5425)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Nat_Osemiring__char__0])]) ).
fof(i_0_2507,plain,
! [X5413] :
( ~ class_Rings_Ocomm__semiring__0(X5413)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X5413)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult])]) ).
fof(i_0_2508,plain,
! [X5424] :
( ~ class_Rings_Ocomm__semiring__0(X5424)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X5424)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring])]) ).
fof(i_0_2509,plain,
! [X5441] :
( ~ class_Rings_Ocomm__semiring__0(X5441)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X5441)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring])]) ).
fof(i_0_2510,plain,
! [X5418] :
( ~ class_Rings_Oidom(X5418)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X5418)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors])]) ).
fof(i_0_2511,plain,
! [X5406] :
( ~ class_Rings_Oidom(X5406)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X5406)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors])]) ).
fof(i_0_2512,plain,
! [X5437] :
( ~ class_Rings_Ocomm__semiring__0(X5437)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X5437)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero])]) ).
fof(i_0_2513,plain,
! [X5399] :
( ~ class_Rings_Olinordered__idom(X5399)
| class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X5399)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs])]) ).
fof(i_0_2514,plain,
! [X5439] :
( ~ class_Rings_Olinordered__idom(X5439)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X5439)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0])]) ).
fof(i_0_2515,plain,
! [X5440] :
( ~ class_Rings_Ocomm__ring__1(X5440)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X5440)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Onumber__ring])]) ).
fof(i_0_2516,plain,
! [X5447] :
( ~ class_Rings_Ocomm__ring__1(X5447)
| class_Int_Onumber(tc_Polynomial_Opoly(X5447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Onumber])]) ).
fof(i_0_2517,plain,
! [X5427] :
( ~ class_Rings_Ocomm__semiring__1(X5427)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X5427)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one])]) ).
fof(i_0_2518,plain,
! [X5421] :
( ~ class_Rings_Olinordered__idom(X5421)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X5421)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom])]) ).
fof(i_0_2519,plain,
! [X5412] :
( ~ class_Rings_Olinordered__idom(X5412)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X5412)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom])]) ).
fof(i_0_2520,plain,
! [X5392] :
( ~ class_Rings_Oidom(X5392)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X5392)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct])]) ).
fof(i_0_2521,plain,
! [X5419] :
( ~ class_Groups_Ocomm__monoid__add(X5419)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X5419)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add])]) ).
fof(i_0_2522,plain,
! [X5433] :
( ~ class_Groups_Ocomm__monoid__add(X5433)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X5433)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add])]) ).
fof(i_0_2523,plain,
! [X5393] :
( ~ class_Rings_Olinordered__idom(X5393)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X5393)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add])]) ).
fof(i_0_2524,plain,
! [X5400] :
( ~ class_Rings_Olinordered__idom(X5400)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X5400)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add])]) ).
fof(i_0_2525,plain,
! [X5401] :
( ~ class_Rings_Olinordered__idom(X5401)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X5401)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add])]) ).
fof(i_0_2526,plain,
! [X5409] :
( ~ class_Rings_Olinordered__idom(X5409)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X5409)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add])]) ).
fof(i_0_2527,plain,
! [X5426] :
( ~ class_Groups_Oab__group__add(X5426)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X5426)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add])]) ).
fof(i_0_2528,plain,
! [X5436] :
( ~ class_Groups_Oab__group__add(X5436)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X5436)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add])]) ).
fof(i_0_2529,plain,
! [X5445] :
( ~ class_Groups_Ozero(X5445)
| class_Groups_Ozero(tc_Polynomial_Opoly(X5445)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero])]) ).
fof(i_0_2530,plain,
! [X5434] :
( ~ class_Rings_Ocomm__semiring__1(X5434)
| class_Rings_Osemiring__1(tc_Polynomial_Opoly(X5434)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__1])]) ).
fof(i_0_2531,plain,
! [X5448] :
( ~ class_Rings_Ocomm__semiring__1(X5448)
| class_Groups_Oone(tc_Polynomial_Opoly(X5448)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone])]) ).
fof(i_0_2532,plain,
! [X5422] :
( ~ class_Rings_Ocomm__semiring__1(X5422)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X5422)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])]) ).
fof(i_0_2533,plain,
! [X5415] :
( ~ class_Groups_Ocomm__monoid__add(X5415)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X5415)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add])]) ).
fof(i_0_2534,plain,
! [X5402] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5402)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X5402)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add])]) ).
fof(i_0_2535,plain,
! [X5410] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5410)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X5410)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add])]) ).
fof(i_0_2536,plain,
! [X5438] :
( ~ class_Rings_Olinordered__idom(X5438)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X5438)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder])]) ).
fof(i_0_2537,plain,
! [X5442] :
( ~ class_Rings_Olinordered__idom(X5442)
| class_Orderings_Oord(tc_Polynomial_Opoly(X5442)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord])]) ).
fof(i_0_2538,plain,
! [X5430] :
( ~ class_Rings_Olinordered__idom(X5430)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X5430)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder])]) ).
fof(i_0_2539,plain,
! [X5398] :
( ~ class_Rings_Olinordered__idom(X5398)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X5398)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add])]) ).
fof(i_0_2540,plain,
! [X5394] :
( ~ class_Rings_Olinordered__idom(X5394)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X5394)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le])]) ).
fof(i_0_2541,plain,
! [X5429] :
( ~ class_Rings_Olinordered__idom(X5429)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X5429)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder])]) ).
fof(i_0_2542,plain,
! [X3940] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3940) = X3940,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
fof(i_0_2543,plain,
~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_simplification,[status(thm)],[fact_not__neg__0]) ).
fof(i_0_2544,plain,
~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_simplification,[status(thm)],[fact_not__neg__1]) ).
cnf(i_0_2545,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,esk46_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_1472]),
[final] ).
cnf(i_0_2546,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4),hAPP(X2,X3))
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk5_4(X3,X4,X2,X1)),hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_4(X3,X4,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1473,c_0_1474]),
[final] ).
cnf(i_0_2547,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),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_1475]),
[final] ).
cnf(i_0_2548,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X2)),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_1476]),
[final] ).
cnf(i_0_2549,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_1477]),
[final] ).
cnf(i_0_2550,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_1478]),
[final] ).
cnf(i_0_2551,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1479,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2552,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_1480]),
[final] ).
cnf(i_0_2553,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_1481]),
[final] ).
cnf(i_0_2554,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_1482]),
[final] ).
cnf(i_0_2555,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_1483]),
[final] ).
cnf(i_0_2556,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_1484]),
[final] ).
cnf(i_0_2557,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_1485]),
[final] ).
cnf(i_0_2558,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_1486]),
[final] ).
cnf(i_0_2559,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_1487]),
[final] ).
cnf(i_0_2560,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_1480]),
[final] ).
cnf(i_0_2561,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_1481]),
[final] ).
cnf(i_0_2562,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_1482]),
[final] ).
cnf(i_0_2563,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_1483]),
[final] ).
cnf(i_0_2564,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_1484]),
[final] ).
cnf(i_0_2565,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_1485]),
[final] ).
cnf(i_0_2566,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_1486]),
[final] ).
cnf(i_0_2567,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_1487]),
[final] ).
cnf(i_0_2568,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(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(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1488]),
[final] ).
cnf(i_0_2569,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),esk70_2(X2,X1)),X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
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(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_1490]),
[final] ).
cnf(i_0_2571,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_1491,c_0_1474]),c_0_1474]),c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2572,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_1492]),
[final] ).
cnf(i_0_2573,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_1493]),
[final] ).
cnf(i_0_2574,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,esk64_3(X2,X1,X3),X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ hBOOL(hAPP(X1,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1494]),
[final] ).
cnf(i_0_2575,plain,
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
| ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,esk65_3(X2,X1,X3),X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ hBOOL(hAPP(X1,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1495]),
[final] ).
cnf(i_0_2576,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_1496,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2577,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_1497,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2578,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk71_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_1498,c_0_1474]),
[final] ).
cnf(i_0_2579,plain,
c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(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_Complex_Ocomplex),c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2)),c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1499,c_0_1500]),c_0_1500]),c_0_1500]),c_0_1474]),
[final] ).
cnf(i_0_2580,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk40_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,esk39_3(X3,X2,X1))),X1) ),
inference(rw,[status(thm)],[i_0_1501,c_0_1474]),
[final] ).
cnf(i_0_2581,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk36_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,esk35_3(X3,X2,X1))),X1) ),
inference(rw,[status(thm)],[i_0_1502,c_0_1474]),
[final] ).
cnf(i_0_2582,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk42_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,esk41_3(X2,X1,X4))),hAPP(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_1503,c_0_1474]),
[final] ).
cnf(i_0_2583,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk38_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,esk37_3(X2,X1,X4))),hAPP(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_1504,c_0_1474]),
[final] ).
cnf(i_0_2584,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_1505]),
[final] ).
cnf(i_0_2585,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_1506]),
[final] ).
cnf(i_0_2586,plain,
( hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2587,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))),esk67_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2588,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))),esk62_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2589,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk42_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,esk41_3(X1,X2,X3))),hAPP(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_1510,c_0_1474]),
[final] ).
cnf(i_0_2590,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk38_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,esk37_3(X1,X2,X3))),hAPP(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_1511,c_0_1474]),
[final] ).
cnf(i_0_2591,plain,
( hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2592,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))))
| ~ hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2593,plain,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk48_3(X2,X1,X3))),hAPP(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_1512,c_0_1474]),
[final] ).
cnf(i_0_2594,plain,
( c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk50_3(X2,X1,X3))),hAPP(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_1513,c_0_1474]),
[final] ).
cnf(i_0_2595,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_1514]),
[final] ).
cnf(i_0_2596,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_1515]),
[final] ).
cnf(i_0_2597,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_1516,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2598,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_1517]),
[final] ).
cnf(i_0_2599,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_1518]),
[final] ).
cnf(i_0_2600,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_1519]),
[final] ).
cnf(i_0_2601,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_1520]),
[final] ).
cnf(i_0_2602,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),hAPP(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_1521]),
[final] ).
cnf(i_0_2603,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk75_3(X2,X1,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))) ),
inference(rw,[status(thm)],[i_0_1522,c_0_1474]),
[final] ).
cnf(i_0_2604,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_1523,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2605,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_1524,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2606,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_1525]),
[final] ).
cnf(i_0_2607,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk75_3(X2,X1,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))) ),
inference(rw,[status(thm)],[i_0_1526,c_0_1474]),
[final] ).
cnf(i_0_2608,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_1527]),
[final] ).
cnf(i_0_2609,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_1528,c_0_1474]),
[final] ).
cnf(i_0_2610,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_1517]),
[final] ).
cnf(i_0_2611,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_1518]),
[final] ).
cnf(i_0_2612,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_1519]),
[final] ).
cnf(i_0_2613,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_1520]),
[final] ).
cnf(i_0_2614,plain,
( hBOOL(hAPP(X4,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)))
| ~ hBOOL(hAPP(X4,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,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)))) ),
inference(rw,[status(thm)],[i_0_1529,c_0_1474]),
[final] ).
cnf(i_0_2615,plain,
( hBOOL(hAPP(X1,esk65_3(X2,X1,X3)))
| hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ hBOOL(hAPP(X1,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1495]),
[final] ).
cnf(i_0_2616,plain,
( hBOOL(hAPP(X1,esk64_3(X2,X1,X3)))
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ hBOOL(hAPP(X1,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1494]),
[final] ).
cnf(i_0_2617,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_1530]),
[final] ).
cnf(i_0_2618,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,esk46_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_1472]),
[final] ).
cnf(i_0_2619,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk79_3(X1,X2,X3)),esk80_3(X1,X2,X3))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk77_3(X1,X2,X3)),esk78_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2620,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_1532]),
[final] ).
cnf(i_0_2621,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_1533]),
[final] ).
cnf(i_0_2622,plain,
( c_SEQ_OBseq(X1,X3)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X3,esk54_3(X3,X2,X1))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1534]),
[final] ).
cnf(i_0_2623,plain,
( c_SEQ_OBseq(X2,X3)
| ~ 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,esk52_3(X3,X2,X1))),X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1535]),
[final] ).
cnf(i_0_2624,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk79_3(X1,X2,X3)),esk80_3(X1,X2,X3))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk77_3(X1,X2,X3)),esk78_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2625,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_1536]),
[final] ).
cnf(i_0_2626,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk79_3(X1,X2,X3)),esk80_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk77_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2627,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk77_3(X2,X3,X1)),esk78_3(X2,X3,X1))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk79_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2628,plain,
( X2 = c_Divides_Odiv__class_Odiv(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__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,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)))) ),
inference(rw,[status(thm)],[i_0_1537,c_0_1474]),
[final] ).
cnf(i_0_2629,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_1538]),
[final] ).
cnf(i_0_2630,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_1539]),
[final] ).
cnf(i_0_2631,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2632,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_1540]),
[final] ).
cnf(i_0_2633,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_1540]),
[final] ).
cnf(i_0_2634,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_1541]),
[final] ).
cnf(i_0_2635,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_1542,c_0_1474]),
[final] ).
cnf(i_0_2636,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk79_3(X1,X2,X3)),esk80_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk77_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2637,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk77_3(X2,X3,X1)),esk78_3(X2,X3,X1))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk79_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2638,plain,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk79_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk77_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2639,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_1543]),
[final] ).
cnf(i_0_2640,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_1544,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2641,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X2)),esk33_3(X4,X3,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1545]),
[final] ).
cnf(i_0_2642,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X1)),esk33_3(X2,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1545]),
[final] ).
cnf(i_0_2643,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk79_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk77_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2644,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_1546]),
[final] ).
cnf(i_0_2645,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_1547]),
[final] ).
cnf(i_0_2646,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1548]),
[final] ).
cnf(i_0_2647,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_1549,c_0_1474]),c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2648,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_1550,c_0_1474]),c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2649,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,X3)),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))),X4)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1551]),
[final] ).
cnf(i_0_2650,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk21_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,esk21_2(X2,X1))) ),
inference(rw,[status(thm)],[i_0_1552,c_0_1474]),
[final] ).
cnf(i_0_2651,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk15_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,esk15_2(X2,X1))) ),
inference(rw,[status(thm)],[i_0_1553,c_0_1474]),
[final] ).
cnf(i_0_2652,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk22_2(X2,X1)),hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk22_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1554,c_0_1474]),
[final] ).
cnf(i_0_2653,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk14_2(X2,X1)),hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk14_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1555,c_0_1474]),
[final] ).
cnf(i_0_2654,plain,
( c_SEQ_Oincseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk16_2(X2,X1)),hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk16_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1556,c_0_1474]),
[final] ).
cnf(i_0_2655,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1557]),
[final] ).
cnf(i_0_2656,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_1558]),
[final] ).
cnf(i_0_2657,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk75_3(X1,X2,X3)),X2)
| hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1287]),
[final] ).
cnf(i_0_2658,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_1559]),
[final] ).
cnf(i_0_2659,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk73_3(X2,X1,X3)),esk74_3(X2,X1,X3))
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2660,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1561]),
[final] ).
cnf(i_0_2661,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk77_3(X1,X2,X3)),esk78_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2662,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk79_3(X1,X2,X3)),esk80_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2663,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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_1562]),
[final] ).
cnf(i_0_2664,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk79_3(X1,X2,X3)),esk80_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X1,X2,X3),X2)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2665,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk80_3(X2,X1,X3))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk77_3(X2,X1,X3)),esk78_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2666,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk75_3(X1,X2,X3)),X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1287]),
[final] ).
cnf(i_0_2667,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_1563]),
[final] ).
cnf(i_0_2668,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_1564]),
[final] ).
cnf(i_0_2669,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_1565,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2670,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_1566,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2671,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X3 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X2)
| ~ hBOOL(hAPP(X5,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2672,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_1567,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2673,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk73_3(X2,X1,X3)),esk74_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2674,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_1568,c_0_1474]),
[final] ).
cnf(i_0_2675,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),X4))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1569]),
[final] ).
cnf(i_0_2676,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),X4))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1570]),
[final] ).
cnf(i_0_2677,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk77_3(X1,X2,X3)),esk78_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2678,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk79_3(X1,X2,X3)),esk80_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2679,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_1571]),
[final] ).
cnf(i_0_2680,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_1572]),
[final] ).
cnf(i_0_2681,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_1573,c_0_1474]),c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2682,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk79_3(X1,X2,X3)),esk80_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X1,X2,X3),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2683,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk80_3(X2,X1,X3))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk77_3(X2,X1,X3)),esk78_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2684,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(X2,X4))
| ~ class_Orderings_Oorder(X1)
| ~ c_SEQ_Omonoseq(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1574,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2685,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk73_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2686,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk26_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_2687,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk25_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1576]),
[final] ).
cnf(i_0_2688,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_2689,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_1578,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2690,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_1579,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2691,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,esk26_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_2692,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,esk25_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1576]),
[final] ).
cnf(i_0_2693,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Int_Onumber__class_Onumber__of(X1,X4)) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Int_Onumber__class_Onumber__of(X1,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1580]),
[final] ).
cnf(i_0_2694,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Int_Onumber__class_Onumber__of(X1,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Int_Onumber__class_Onumber__of(X1,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_2695,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,v_g____(hAPP(v_f____,X2)),v_z____)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk43_1(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2696,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_1583]),
[final] ).
cnf(i_0_2697,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,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_1584]),
[final] ).
cnf(i_0_2698,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk77_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2699,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X2,X3,X1))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk79_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2700,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),esk71_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_1279]),
[final] ).
cnf(i_0_2701,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X2,X3,X1),X3)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk79_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2702,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk80_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk77_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2703,plain,
( hBOOL(hAPP(X1,esk75_3(X2,X3,X1)))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1287]),
[final] ).
cnf(i_0_2704,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_1585]),
[final] ).
cnf(i_0_2705,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_1586]),
[final] ).
cnf(i_0_2706,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_1587,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2707,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,X3,hAPP(X2,X4))
| ~ class_Rings_Osemiring__1(X1) ),
inference(rw,[status(thm)],[i_0_1588,c_0_1474]),
[final] ).
cnf(i_0_2708,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk79_3(X1,X2,X3)),esk80_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2709,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk77_3(X2,X1,X3)),esk78_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2710,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_1589]),
[final] ).
cnf(i_0_2711,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1548]),
[final] ).
cnf(i_0_2712,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1548]),
[final] ).
cnf(i_0_2713,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_1590]),
[final] ).
cnf(i_0_2714,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_1591]),
[final] ).
cnf(i_0_2715,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_1592]),
[final] ).
cnf(i_0_2716,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_1593]),
[final] ).
cnf(i_0_2717,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_1594]),
[final] ).
cnf(i_0_2718,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_1595]),
[final] ).
cnf(i_0_2719,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_1596]),
[final] ).
cnf(i_0_2720,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_1597]),
[final] ).
cnf(i_0_2721,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_1598]),
[final] ).
cnf(i_0_2722,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1) = X4
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1599]),
[final] ).
cnf(i_0_2723,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk73_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2724,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_1600]),
[final] ).
cnf(i_0_2725,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_1601]),
[final] ).
cnf(i_0_2726,plain,
( hBOOL(hAPP(X1,esk75_3(X2,X3,X1)))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1287]),
[final] ).
cnf(i_0_2727,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2728,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2729,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1602]),
[final] ).
cnf(i_0_2730,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk77_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2731,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X2,X3,X1))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk79_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2732,plain,
( hBOOL(hAPP(X5,X4))
| ~ 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)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2)
| ~ epred1_3(X5,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2733,plain,
( hBOOL(hAPP(X5,X4))
| ~ 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,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2)
| ~ epred1_3(X5,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2734,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X2,X3,X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk79_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2735,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk80_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk77_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2736,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_1540]),
[final] ).
cnf(i_0_2737,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ 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),X1) ),
inference(rw,[status(thm)],[i_0_1603,c_0_1474]),
[final] ).
cnf(i_0_2738,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_1538]),
[final] ).
cnf(i_0_2739,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_1538]),
[final] ).
cnf(i_0_2740,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_1604]),
[final] ).
cnf(i_0_2741,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_1605,c_0_1474]),
[final] ).
cnf(i_0_2742,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk79_3(X1,X2,X3)),esk80_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2743,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk77_3(X2,X1,X3)),esk78_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2744,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_1606]),
[final] ).
cnf(i_0_2745,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_1607,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2746,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_1608,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2747,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_1609,c_0_1474]),
[final] ).
cnf(i_0_2748,plain,
( c_SEQ_Osubseq(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,esk30_1(X1)),hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk30_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1610,c_0_1474]),
[final] ).
cnf(i_0_2749,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_1611]),
[final] ).
cnf(i_0_2750,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_1612]),
[final] ).
cnf(i_0_2751,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_1613]),
[final] ).
cnf(i_0_2752,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_1614]),
[final] ).
cnf(i_0_2753,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_1615]),
[final] ).
cnf(i_0_2754,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_1616]),
[final] ).
cnf(i_0_2755,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_1617]),
[final] ).
cnf(i_0_2756,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_1618]),
[final] ).
cnf(i_0_2757,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_1619]),
[final] ).
cnf(i_0_2758,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_1620]),
[final] ).
cnf(i_0_2759,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_1621]),
[final] ).
cnf(i_0_2760,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_1622]),
[final] ).
cnf(i_0_2761,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,v_g____(hAPP(v_f____,X1)),v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk45_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2762,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,v_g____(hAPP(v_f____,X1)),v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk44_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2763,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,v_g____(hAPP(v_f____,X1)),v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1625]),
[final] ).
cnf(i_0_2764,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_1626]),
[final] ).
cnf(i_0_2765,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_1627]),
[final] ).
cnf(i_0_2766,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_1628]),
[final] ).
cnf(i_0_2767,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_1629]),
[final] ).
cnf(i_0_2768,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)),X3)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2769,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)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1631,c_0_1474]),c_0_1632]),
[final] ).
cnf(i_0_2770,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| 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),X2) ),
inference(rw,[status(thm)],[i_0_1633,c_0_1474]),
[final] ).
cnf(i_0_2771,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| 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),X1) ),
inference(rw,[status(thm)],[i_0_1634,c_0_1474]),
[final] ).
cnf(i_0_2772,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk79_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2773,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| epred1_3(X2,X1,X3)
| ~ hBOOL(hAPP(X2,esk77_3(X3,X1,X2)))
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2774,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,hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2775,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1) = X4
| ~ 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)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1599]),
[final] ).
cnf(i_0_2776,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2),X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2777,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_1637]),
[final] ).
cnf(i_0_2778,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_1638]),
[final] ).
cnf(i_0_2779,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_1639]),
[final] ).
cnf(i_0_2780,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_1640]),
[final] ).
cnf(i_0_2781,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_1641]),
[final] ).
cnf(i_0_2782,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_1642]),
[final] ).
cnf(i_0_2783,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_1643]),
[final] ).
cnf(i_0_2784,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_1644]),
[final] ).
cnf(i_0_2785,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Odivide(X1,X3,X2)),X4) = c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1645]),
[final] ).
cnf(i_0_2786,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| X3 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(rw,[status(thm)],[i_0_1646,c_0_1474]),
[final] ).
cnf(i_0_2787,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_1647]),
[final] ).
cnf(i_0_2788,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_1648]),
[final] ).
cnf(i_0_2789,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)),esk68_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1649]),
[final] ).
cnf(i_0_2790,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)),esk61_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_2791,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_1651]),
[final] ).
cnf(i_0_2792,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)),esk69_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_2793,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)),esk63_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_2794,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1654]),
[final] ).
cnf(i_0_2795,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1655]),
[final] ).
cnf(i_0_2796,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[i_0_1656,c_0_1474]),
[final] ).
cnf(i_0_2797,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_1657]),
[final] ).
cnf(i_0_2798,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_1658]),
[final] ).
cnf(i_0_2799,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_1659]),
[final] ).
cnf(i_0_2800,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_1660]),
[final] ).
cnf(i_0_2801,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_1661]),
[final] ).
cnf(i_0_2802,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_1662]),
[final] ).
cnf(i_0_2803,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_1663]),
[final] ).
cnf(i_0_2804,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_1648]),
[final] ).
cnf(i_0_2805,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_1647]),
[final] ).
cnf(i_0_2806,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_1647]),
[final] ).
cnf(i_0_2807,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_1648]),
[final] ).
cnf(i_0_2808,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_1546]),
[final] ).
cnf(i_0_2809,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_1547]),
[final] ).
cnf(i_0_2810,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1664,c_0_1474]),c_0_1665]),
[final] ).
cnf(i_0_2811,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_1666,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2812,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2))),
inference(split_conjunct,[status(thm)],[i_0_1667]),
[final] ).
cnf(i_0_2813,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_1648]),
[final] ).
cnf(i_0_2814,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_1647]),
[final] ).
cnf(i_0_2815,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_1668]),
[final] ).
cnf(i_0_2816,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_1669]),
[final] ).
cnf(i_0_2817,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_1670]),
[final] ).
cnf(i_0_2818,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_1671]),
[final] ).
cnf(i_0_2819,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_1672]),
[final] ).
cnf(i_0_2820,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk47_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(rw,[status(thm)],[i_0_1673,c_0_1474]),
[final] ).
cnf(i_0_2821,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk49_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OBseq(X1,X2) ),
inference(rw,[status(thm)],[i_0_1674,c_0_1474]),
[final] ).
cnf(i_0_2822,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X1) = X4
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1599]),
[final] ).
cnf(i_0_2823,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_1590]),
[final] ).
cnf(i_0_2824,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_1591]),
[final] ).
cnf(i_0_2825,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2826,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1676]),
[final] ).
cnf(i_0_2827,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2828,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1678]),
[final] ).
cnf(i_0_2829,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_1679]),
[final] ).
cnf(i_0_2830,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_1680]),
[final] ).
cnf(i_0_2831,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_1681]),
[final] ).
cnf(i_0_2832,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_1682]),
[final] ).
cnf(i_0_2833,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_1683]),
[final] ).
cnf(i_0_2834,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_1684]),
[final] ).
cnf(i_0_2835,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_1685]),
[final] ).
cnf(i_0_2836,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_1686]),
[final] ).
cnf(i_0_2837,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_1687]),
[final] ).
cnf(i_0_2838,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_1688]),
[final] ).
cnf(i_0_2839,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_1689]),
[final] ).
cnf(i_0_2840,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_1690]),
[final] ).
cnf(i_0_2841,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_1691]),
[final] ).
cnf(i_0_2842,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk79_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2843,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X2,X1,X3)
| ~ hBOOL(hAPP(X2,esk77_3(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2844,plain,
( c_RComplete_Onatfloor(X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_2845,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_1575]),
[final] ).
cnf(i_0_2846,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_1576]),
[final] ).
cnf(i_0_2847,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk60_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[i_0_1693,c_0_1474]),
[final] ).
cnf(i_0_2848,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_1575]),
[final] ).
cnf(i_0_2849,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_1576]),
[final] ).
cnf(i_0_2850,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_1694]),
[final] ).
cnf(i_0_2851,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_1694]),
[final] ).
cnf(i_0_2852,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_1695]),
[final] ).
cnf(i_0_2853,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_1696]),
[final] ).
cnf(i_0_2854,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_1697]),
[final] ).
cnf(i_0_2855,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_1698]),
[final] ).
cnf(i_0_2856,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_1699]),
[final] ).
cnf(i_0_2857,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_1700,c_0_1474]),
[final] ).
cnf(i_0_2858,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_1701]),
[final] ).
cnf(i_0_2859,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_1702]),
[final] ).
cnf(i_0_2860,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_1703]),
[final] ).
cnf(i_0_2861,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_1704]),
[final] ).
cnf(i_0_2862,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_1705]),
[final] ).
cnf(i_0_2863,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_1706]),
[final] ).
cnf(i_0_2864,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_1707]),
[final] ).
cnf(i_0_2865,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_1708]),
[final] ).
cnf(i_0_2866,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_1709]),
[final] ).
cnf(i_0_2867,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_1710,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2868,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_1711,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2869,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_1712,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2870,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_1713,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2871,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_1714]),
[final] ).
cnf(i_0_2872,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_1715]),
[final] ).
cnf(i_0_2873,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_1585]),
[final] ).
cnf(i_0_2874,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_1716]),
[final] ).
cnf(i_0_2875,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_1717,c_0_1474]),
[final] ).
cnf(i_0_2876,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_1718]),
[final] ).
cnf(i_0_2877,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_1719]),
[final] ).
cnf(i_0_2878,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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1720]),
[final] ).
cnf(i_0_2879,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_2880,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_1722]),
[final] ).
cnf(i_0_2881,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk26_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_1575]),
[final] ).
cnf(i_0_2882,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk25_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_1576]),
[final] ).
cnf(i_0_2883,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk74_3(X1,X2,X3),X1)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2884,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_1723]),
[final] ).
cnf(i_0_2885,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_1724]),
[final] ).
cnf(i_0_2886,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_1725]),
[final] ).
cnf(i_0_2887,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_1726]),
[final] ).
cnf(i_0_2888,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk26_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_1575]),
[final] ).
cnf(i_0_2889,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk25_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_1576]),
[final] ).
cnf(i_0_2890,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_1727]),
[final] ).
cnf(i_0_2891,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_1728]),
[final] ).
cnf(i_0_2892,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_1729]),
[final] ).
cnf(i_0_2893,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_1647]),
[final] ).
cnf(i_0_2894,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_1730]),
[final] ).
cnf(i_0_2895,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_1648]),
[final] ).
cnf(i_0_2896,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_1731]),
[final] ).
cnf(i_0_2897,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_1732]),
[final] ).
cnf(i_0_2898,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_1617]),
[final] ).
cnf(i_0_2899,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_1733]),
[final] ).
cnf(i_0_2900,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_1734]),
[final] ).
cnf(i_0_2901,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_1735]),
[final] ).
cnf(i_0_2902,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_1736]),
[final] ).
cnf(i_0_2903,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_1620]),
[final] ).
cnf(i_0_2904,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_1647]),
[final] ).
cnf(i_0_2905,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_1737]),
[final] ).
cnf(i_0_2906,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_1648]),
[final] ).
cnf(i_0_2907,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_1738]),
[final] ).
cnf(i_0_2908,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_1621]),
[final] ).
cnf(i_0_2909,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_1739]),
[final] ).
cnf(i_0_2910,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_1740]),
[final] ).
cnf(i_0_2911,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_1622]),
[final] ).
cnf(i_0_2912,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_1741]),
[final] ).
cnf(i_0_2913,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_1742]),
[final] ).
cnf(i_0_2914,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_1743]),
[final] ).
cnf(i_0_2915,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_1744]),
[final] ).
cnf(i_0_2916,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_1745]),
[final] ).
cnf(i_0_2917,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_1746]),
[final] ).
cnf(i_0_2918,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_1626]),
[final] ).
cnf(i_0_2919,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_1747]),
[final] ).
cnf(i_0_2920,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_1628]),
[final] ).
cnf(i_0_2921,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,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),X3)
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_2922,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ 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__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_2923,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ 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__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_2924,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ 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__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_2925,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(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),esk78_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2926,plain,
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk31_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_1749]),
[final] ).
cnf(i_0_2927,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_1750]),
[final] ).
cnf(i_0_2928,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_1751,c_0_1474]),
[final] ).
cnf(i_0_2929,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X1,X2,X3),X2)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2930,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk80_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2931,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_1752]),
[final] ).
cnf(i_0_2932,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2),c_Divides_Odiv__class_Odiv(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__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1753]),
[final] ).
cnf(i_0_2933,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_1754]),
[final] ).
cnf(i_0_2934,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk80_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X2,X1,X3),X1)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2935,plain,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_2936,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_1756]),
[final] ).
cnf(i_0_2937,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_1757]),
[final] ).
cnf(i_0_2938,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_1758]),
[final] ).
cnf(i_0_2939,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_1759]),
[final] ).
cnf(i_0_2940,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_1760]),
[final] ).
cnf(i_0_2941,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_1761]),
[final] ).
cnf(i_0_2942,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_1761]),
[final] ).
cnf(i_0_2943,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_1762,c_0_1474]),
[final] ).
cnf(i_0_2944,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_1763,c_0_1474]),
[final] ).
cnf(i_0_2945,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_2946,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_1765]),
[final] ).
cnf(i_0_2947,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_1766]),
[final] ).
cnf(i_0_2948,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_1767]),
[final] ).
cnf(i_0_2949,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_1768]),
[final] ).
cnf(i_0_2950,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_1769]),
[final] ).
cnf(i_0_2951,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_1770]),
[final] ).
cnf(i_0_2952,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_1771]),
[final] ).
cnf(i_0_2953,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_1772]),
[final] ).
cnf(i_0_2954,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_1773]),
[final] ).
cnf(i_0_2955,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_1774]),
[final] ).
cnf(i_0_2956,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(X1,X2)),X3) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3)),X2)),
inference(split_conjunct,[status(thm)],[i_0_1775]),
[final] ).
cnf(i_0_2957,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_1771]),
[final] ).
cnf(i_0_2958,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_1770]),
[final] ).
cnf(i_0_2959,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_1776]),
[final] ).
cnf(i_0_2960,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_1777]),
[final] ).
cnf(i_0_2961,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_1778]),
[final] ).
cnf(i_0_2962,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_1779]),
[final] ).
cnf(i_0_2963,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk32_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_1780]),
[final] ).
cnf(i_0_2964,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk34_1(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(rw,[status(thm)],[i_0_1781,c_0_1474]),
[final] ).
cnf(i_0_2965,plain,
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2966,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X2,X4))
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X6),hAPP(X2,X5))
| ~ c_SEQ_Omonoseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X6)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_2967,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_1783,c_0_1474]),
[final] ).
cnf(i_0_2968,plain,
( c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),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_1784]),
[final] ).
cnf(i_0_2969,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_1785,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_2970,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_1786]),
[final] ).
cnf(i_0_2971,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_1787]),
[final] ).
cnf(i_0_2972,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_1788]),
[final] ).
cnf(i_0_2973,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_1789]),
[final] ).
cnf(i_0_2974,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_1680]),
[final] ).
cnf(i_0_2975,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_1770]),
[final] ).
cnf(i_0_2976,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_1790]),
[final] ).
cnf(i_0_2977,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_1771]),
[final] ).
cnf(i_0_2978,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_1682]),
[final] ).
cnf(i_0_2979,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_1791]),
[final] ).
cnf(i_0_2980,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_1683]),
[final] ).
cnf(i_0_2981,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_1684]),
[final] ).
cnf(i_0_2982,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_1686]),
[final] ).
cnf(i_0_2983,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_1792]),
[final] ).
cnf(i_0_2984,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_1793]),
[final] ).
cnf(i_0_2985,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_1794]),
[final] ).
cnf(i_0_2986,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_1793]),
[final] ).
cnf(i_0_2987,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_1794]),
[final] ).
cnf(i_0_2988,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(rw,[status(thm)],[i_0_1795,c_0_1632]),
[final] ).
cnf(i_0_2989,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk74_3(X1,X2,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2990,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_1796]),
[final] ).
cnf(i_0_2991,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_1797]),
[final] ).
cnf(i_0_2992,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_1798]),
[final] ).
cnf(i_0_2993,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_1799]),
[final] ).
cnf(i_0_2994,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_1800]),
[final] ).
cnf(i_0_2995,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_1801]),
[final] ).
cnf(i_0_2996,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_1772]),
[final] ).
cnf(i_0_2997,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_1802]),
[final] ).
cnf(i_0_2998,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_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),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_1803]),
[final] ).
cnf(i_0_2999,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_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),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_1804]),
[final] ).
cnf(i_0_3000,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_1805]),
[final] ).
cnf(i_0_3001,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_1772]),
[final] ).
cnf(i_0_3002,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_1806]),
[final] ).
cnf(i_0_3003,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,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_1807]),
[final] ).
cnf(i_0_3004,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_1808]),
[final] ).
cnf(i_0_3005,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_1808]),
[final] ).
cnf(i_0_3006,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_1808]),
[final] ).
cnf(i_0_3007,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_1809]),
[final] ).
cnf(i_0_3008,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_1809]),
[final] ).
cnf(i_0_3009,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_1809]),
[final] ).
cnf(i_0_3010,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_1809]),
[final] ).
cnf(i_0_3011,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_1808]),
[final] ).
cnf(i_0_3012,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(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),esk78_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3013,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3014,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_1811]),
[final] ).
cnf(i_0_3015,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_1812]),
[final] ).
cnf(i_0_3016,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_1813]),
[final] ).
cnf(i_0_3017,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_1814]),
[final] ).
cnf(i_0_3018,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X1,X2,X3),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3019,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk80_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk78_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3020,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk80_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk78_3(X2,X1,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3021,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_1815]),
[final] ).
cnf(i_0_3022,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,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_1816]),
[final] ).
cnf(i_0_3023,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_1817]),
[final] ).
cnf(i_0_3024,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_1817]),
[final] ).
cnf(i_0_3025,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_3026,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_3027,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_1819,c_0_1474]),
[final] ).
cnf(i_0_3028,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_1820,c_0_1474]),
[final] ).
cnf(i_0_3029,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(split_conjunct,[status(thm)],[fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096]),
[final] ).
cnf(i_0_3030,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_1821,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3031,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_1822,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3032,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_1823]),
[final] ).
cnf(i_0_3033,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_1824]),
[final] ).
cnf(i_0_3034,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_1825]),
[final] ).
cnf(i_0_3035,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_1826]),
[final] ).
cnf(i_0_3036,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_1827]),
[final] ).
cnf(i_0_3037,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_1828]),
[final] ).
cnf(i_0_3038,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_1829]),
[final] ).
cnf(i_0_3039,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_1830]),
[final] ).
cnf(i_0_3040,plain,
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_3041,plain,
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1832]),
[final] ).
cnf(i_0_3042,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_1833]),
[final] ).
cnf(i_0_3043,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_1834]),
[final] ).
cnf(i_0_3044,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_1835]),
[final] ).
cnf(i_0_3045,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_1836]),
[final] ).
cnf(i_0_3046,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_1837]),
[final] ).
cnf(i_0_3047,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_1838]),
[final] ).
cnf(i_0_3048,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_1839]),
[final] ).
cnf(i_0_3049,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_1840]),
[final] ).
cnf(i_0_3050,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_1841]),
[final] ).
cnf(i_0_3051,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_1842]),
[final] ).
cnf(i_0_3052,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_1841]),
[final] ).
cnf(i_0_3053,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_1843]),
[final] ).
cnf(i_0_3054,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_1808]),
[final] ).
cnf(i_0_3055,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_1808]),
[final] ).
cnf(i_0_3056,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_1844]),
[final] ).
cnf(i_0_3057,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_1845]),
[final] ).
cnf(i_0_3058,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_1846]),
[final] ).
cnf(i_0_3059,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_1847]),
[final] ).
cnf(i_0_3060,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_1848]),
[final] ).
cnf(i_0_3061,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_1809]),
[final] ).
cnf(i_0_3062,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_1849]),
[final] ).
cnf(i_0_3063,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_1847]),
[final] ).
cnf(i_0_3064,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_1850]),
[final] ).
cnf(i_0_3065,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_1809]),
[final] ).
cnf(i_0_3066,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_1851]),
[final] ).
cnf(i_0_3067,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_1703]),
[final] ).
cnf(i_0_3068,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_1852]),
[final] ).
cnf(i_0_3069,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_1705]),
[final] ).
cnf(i_0_3070,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_1853]),
[final] ).
cnf(i_0_3071,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_1707]),
[final] ).
cnf(i_0_3072,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_1854]),
[final] ).
cnf(i_0_3073,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_1709]),
[final] ).
cnf(i_0_3074,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(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_1855]),
[final] ).
cnf(i_0_3075,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1557]),
[final] ).
cnf(i_0_3076,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_1856,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3077,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_1857,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3078,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_1858,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3079,plain,
( X1 = esk72_2(X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2) != X3
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ 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_3080,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_1860]),
[final] ).
cnf(i_0_3081,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk19_2(X2,X1)),hAPP(X2,esk20_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1861]),
[final] ).
cnf(i_0_3082,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk18_2(X2,X1)),hAPP(X2,esk17_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1862]),
[final] ).
cnf(i_0_3083,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk13_2(X2,X1)),hAPP(X2,esk12_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_3084,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk10_2(X2,X1)),hAPP(X2,esk11_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_3085,plain,
( c_SEQ_Oincseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk8_2(X2,X1)),hAPP(X2,esk9_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3086,plain,
( c_SEQ_Odecseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk7_2(X2,X1)),hAPP(X2,esk6_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1864]),
[final] ).
cnf(i_0_3087,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_1865]),
[final] ).
cnf(i_0_3088,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_1866]),
[final] ).
cnf(i_0_3089,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_1867]),
[final] ).
cnf(i_0_3090,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_1868]),
[final] ).
cnf(i_0_3091,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_1869]),
[final] ).
cnf(i_0_3092,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_1870]),
[final] ).
cnf(i_0_3093,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_1871]),
[final] ).
cnf(i_0_3094,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1872]),
[final] ).
cnf(i_0_3095,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
inference(rw,[status(thm)],[i_0_1873,c_0_1474]),
[final] ).
cnf(i_0_3096,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))
| ~ class_Rings_Oring__1(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1874]),
[final] ).
cnf(i_0_3097,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),X2) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1875,c_0_1500]),c_0_1500]),
[final] ).
cnf(i_0_3098,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_1876]),
[final] ).
cnf(i_0_3099,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_1877]),
[final] ).
cnf(i_0_3100,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_1718]),
[final] ).
cnf(i_0_3101,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_1878]),
[final] ).
cnf(i_0_3102,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_1879]),
[final] ).
cnf(i_0_3103,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X3),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1880]),
[final] ).
cnf(i_0_3104,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_1881]),
[final] ).
cnf(i_0_3105,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_1882]),
[final] ).
cnf(i_0_3106,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_1883]),
[final] ).
cnf(i_0_3107,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_1719]),
[final] ).
cnf(i_0_3108,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_3109,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk24_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_1884,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3110,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1720]),
[final] ).
cnf(i_0_3111,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(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_1721]),
[final] ).
cnf(i_0_3112,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_1885,c_0_1474]),
[final] ).
cnf(i_0_3113,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_1886]),
[final] ).
cnf(i_0_3114,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_1887]),
[final] ).
cnf(i_0_3115,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_1888,c_0_1474]),
[final] ).
cnf(i_0_3116,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_1889,c_0_1474]),
[final] ).
cnf(i_0_3117,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk24_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_1890,c_0_1474]),
[final] ).
cnf(i_0_3118,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3119,plain,
( c_Orderings_Oord__class_Oless(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(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_1892]),
[final] ).
cnf(i_0_3120,plain,
( c_Orderings_Oord__class_Oless(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(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_1804]),
[final] ).
cnf(i_0_3121,plain,
( c_Orderings_Oord__class_Oless(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(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_1803]),
[final] ).
cnf(i_0_3122,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_1893]),
[final] ).
cnf(i_0_3123,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_1894]),
[final] ).
cnf(i_0_3124,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_1802]),
[final] ).
cnf(i_0_3125,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__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3126,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_1896]),
[final] ).
cnf(i_0_3127,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_1805]),
[final] ).
cnf(i_0_3128,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_1897,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3129,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_1898,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3130,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_1899]),
[final] ).
cnf(i_0_3131,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_1900]),
[final] ).
cnf(i_0_3132,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1),X2)
| ~ c_Orderings_Oord__class_Oless(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),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_3133,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_1902]),
[final] ).
cnf(i_0_3134,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_1806]),
[final] ).
cnf(i_0_3135,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X1,X2,X3),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)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3136,plain,
( c_Orderings_Oord__class_Oless(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),esk78_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3137,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ c_SEQ_Osubseq(X1) ),
inference(rw,[status(thm)],[i_0_1903,c_0_1474]),
[final] ).
cnf(i_0_3138,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_1904]),
[final] ).
cnf(i_0_3139,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_1905]),
[final] ).
cnf(i_0_3140,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_1906]),
[final] ).
cnf(i_0_3141,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_1907]),
[final] ).
cnf(i_0_3142,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_1908]),
[final] ).
cnf(i_0_3143,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X1,X2)),c_Complex_Orcis(X3,X4)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3144,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_1910,c_0_1474]),
[final] ).
cnf(i_0_3145,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_3(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1545]),
[final] ).
cnf(i_0_3146,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_1911]),
[final] ).
cnf(i_0_3147,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_1912]),
[final] ).
cnf(i_0_3148,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_1913]),
[final] ).
cnf(i_0_3149,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_1914]),
[final] ).
cnf(i_0_3150,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_1915]),
[final] ).
cnf(i_0_3151,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk80_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3152,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,esk78_3(X2,X1,X3),X1)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3153,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1),
inference(split_conjunct,[status(thm)],[i_0_1916]),
[final] ).
cnf(i_0_3154,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)) = c_Divides_Odiv__class_Odiv(X2,X3,X4)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1917]),
[final] ).
cnf(i_0_3155,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = c_Divides_Odiv__class_Odiv(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_3156,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) = c_Divides_Odiv__class_Odiv(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1919]),
[final] ).
cnf(i_0_3157,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_1920]),
[final] ).
cnf(i_0_3158,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_1921]),
[final] ).
cnf(i_0_3159,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_1922,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3160,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_1923,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3161,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_1924,c_0_1474]),
[final] ).
cnf(i_0_3162,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)))
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_3163,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_1925]),
[final] ).
cnf(i_0_3164,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_1926]),
[final] ).
cnf(i_0_3165,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_1927]),
[final] ).
cnf(i_0_3166,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_1928,c_0_1474]),
[final] ).
cnf(i_0_3167,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_1929,c_0_1474]),
[final] ).
cnf(i_0_3168,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_1930,c_0_1474]),
[final] ).
cnf(i_0_3169,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),X2) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_3170,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_1932]),
[final] ).
cnf(i_0_3171,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_1933,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3172,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_1934,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3173,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1),X2)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(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_1935]),
[final] ).
cnf(i_0_3174,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X2))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Int_Onumber__class_Onumber__of(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_1936]),
[final] ).
cnf(i_0_3175,plain,
( c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_1937]),
[final] ).
cnf(i_0_3176,plain,
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2),hAPP(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_1938]),
[final] ).
cnf(i_0_3177,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_1939]),
[final] ).
cnf(i_0_3178,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_1939]),
[final] ).
cnf(i_0_3179,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_1940]),
[final] ).
cnf(i_0_3180,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_1940]),
[final] ).
cnf(i_0_3181,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,hAPP(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_1941]),
[final] ).
cnf(i_0_3182,plain,
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,hAPP(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_1942]),
[final] ).
cnf(i_0_3183,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1943]),
[final] ).
cnf(i_0_3184,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_RComplete_Onatfloor(X2))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,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_1935]),
[final] ).
cnf(i_0_3185,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(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_1936]),
[final] ).
cnf(i_0_3186,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_1685]),
[final] ).
cnf(i_0_3187,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_1944]),
[final] ).
cnf(i_0_3188,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_1687]),
[final] ).
cnf(i_0_3189,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_1945]),
[final] ).
cnf(i_0_3190,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)
| X2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,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_1289]),
[final] ).
cnf(i_0_3191,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_1946]),
[final] ).
cnf(i_0_3192,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_1947]),
[final] ).
cnf(i_0_3193,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_1948]),
[final] ).
cnf(i_0_3194,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_1949]),
[final] ).
cnf(i_0_3195,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_1950]),
[final] ).
cnf(i_0_3196,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_1951]),
[final] ).
cnf(i_0_3197,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_1952]),
[final] ).
cnf(i_0_3198,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_1953]),
[final] ).
cnf(i_0_3199,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_1954]),
[final] ).
cnf(i_0_3200,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_1955]),
[final] ).
cnf(i_0_3201,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_1956,c_0_1474]),
[final] ).
cnf(i_0_3202,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_1957,c_0_1474]),
[final] ).
cnf(i_0_3203,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_1958,c_0_1474]),
[final] ).
cnf(i_0_3204,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_1959,c_0_1474]),
[final] ).
cnf(i_0_3205,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_1960]),
[final] ).
cnf(i_0_3206,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_1961,c_0_1474]),
[final] ).
cnf(i_0_3207,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_1962,c_0_1474]),
[final] ).
cnf(i_0_3208,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_1963,c_0_1474]),
[final] ).
cnf(i_0_3209,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_1964,c_0_1474]),
[final] ).
cnf(i_0_3210,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ 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)),X2) ),
inference(rw,[status(thm)],[i_0_1965,c_0_1632]),
[final] ).
cnf(i_0_3211,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_1966,c_0_1474]),
[final] ).
cnf(i_0_3212,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_1967]),
[final] ).
cnf(i_0_3213,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_1968]),
[final] ).
cnf(i_0_3214,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_1969,c_0_1474]),
[final] ).
cnf(i_0_3215,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_1970,c_0_1474]),
[final] ).
cnf(i_0_3216,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_1971,c_0_1474]),
[final] ).
cnf(i_0_3217,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk56_1(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_1972]),
[final] ).
cnf(i_0_3218,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_1973]),
[final] ).
cnf(i_0_3219,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_1974]),
[final] ).
cnf(i_0_3220,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_1975]),
[final] ).
cnf(i_0_3221,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(rw,[status(thm)],[i_0_1976,c_0_1474]),
[final] ).
cnf(i_0_3222,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_1977,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3223,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_1978]),
[final] ).
cnf(i_0_3224,plain,
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1287]),
[final] ).
cnf(i_0_3225,plain,
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X1)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_3226,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_1979]),
[final] ).
cnf(i_0_3227,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_1980]),
[final] ).
cnf(i_0_3228,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_1980]),
[final] ).
cnf(i_0_3229,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_1981]),
[final] ).
cnf(i_0_3230,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_1982]),
[final] ).
cnf(i_0_3231,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1983]),
[final] ).
cnf(i_0_3232,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_1984,c_0_1474]),
[final] ).
cnf(i_0_3233,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_1985,c_0_1474]),c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3234,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_1986,c_0_1474]),c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3235,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk29_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_1987,c_0_1474]),
[final] ).
cnf(i_0_3236,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_1988]),
[final] ).
cnf(i_0_3237,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_1988]),
[final] ).
cnf(i_0_3238,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_1989]),
[final] ).
cnf(i_0_3239,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_1990,c_0_1474]),c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3240,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3241,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_1992]),
[final] ).
cnf(i_0_3242,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_1993]),
[final] ).
cnf(i_0_3243,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_1687]),
[final] ).
cnf(i_0_3244,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_1685]),
[final] ).
cnf(i_0_3245,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_3246,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_1761]),
[final] ).
cnf(i_0_3247,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_1926]),
[final] ).
cnf(i_0_3248,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_1926]),
[final] ).
cnf(i_0_3249,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3250,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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1996]),
[final] ).
cnf(i_0_3251,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,hAPP(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_1997]),
[final] ).
cnf(i_0_3252,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_1998]),
[final] ).
cnf(i_0_3253,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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_1818]),
[final] ).
cnf(i_0_3254,plain,
( c_Divides_Odiv__class_Odiv(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1917]),
[final] ).
cnf(i_0_3255,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk80_3(X1,X2,X3),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)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3256,plain,
( c_Orderings_Oord__class_Oless(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),esk78_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3257,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk76_2(X1,X2)),X2) = X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_1999]),
[final] ).
cnf(i_0_3258,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),esk72_2(X1,X2)),X2) = X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_1859]),
[final] ).
cnf(i_0_3259,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk80_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3260,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,esk78_3(X2,X1,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3261,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_1988]),
[final] ).
cnf(i_0_3262,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3263,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_2001,c_0_1632]),
[final] ).
cnf(i_0_3264,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_1906]),
[final] ).
cnf(i_0_3265,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_1907]),
[final] ).
cnf(i_0_3266,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_1908]),
[final] ).
cnf(i_0_3267,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_1904]),
[final] ).
cnf(i_0_3268,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_1905]),
[final] ).
cnf(i_0_3269,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_2002,c_0_1474]),
[final] ).
cnf(i_0_3270,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_2003]),
[final] ).
cnf(i_0_3271,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3272,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_1998]),
[final] ).
cnf(i_0_3273,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(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_1997]),
[final] ).
cnf(i_0_3274,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_2005,c_0_1474]),
[final] ).
cnf(i_0_3275,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3276,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2007]),
[final] ).
cnf(i_0_3277,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_3278,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_2009]),
[final] ).
cnf(i_0_3279,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_2010]),
[final] ).
cnf(i_0_3280,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_2011]),
[final] ).
cnf(i_0_3281,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_2012]),
[final] ).
cnf(i_0_3282,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_2013]),
[final] ).
cnf(i_0_3283,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3284,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_2014]),
[final] ).
cnf(i_0_3285,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2)) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2015,c_0_1500]),c_0_1500]),c_0_1500]),
[final] ).
cnf(i_0_3286,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3287,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_1989]),
[final] ).
cnf(i_0_3288,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_1920]),
[final] ).
cnf(i_0_3289,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_1921]),
[final] ).
cnf(i_0_3290,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2017]),
[final] ).
cnf(i_0_3291,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_2018]),
[final] ).
cnf(i_0_3292,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk76_2(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_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3293,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk72_2(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_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1859]),
[final] ).
cnf(i_0_3294,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_2019]),
[final] ).
cnf(i_0_3295,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) = X3
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2020]),
[final] ).
cnf(i_0_3296,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_2021]),
[final] ).
cnf(i_0_3297,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk31_2(X2,X3))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3298,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_2022,c_0_1474]),
[final] ).
cnf(i_0_3299,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_2023,c_0_1474]),
[final] ).
cnf(i_0_3300,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_2024,c_0_1474]),
[final] ).
cnf(i_0_3301,plain,
( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk57_1(X2))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2025]),
[final] ).
cnf(i_0_3302,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_2026]),
[final] ).
cnf(i_0_3303,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2027]),
[final] ).
cnf(i_0_3304,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_2028,c_0_1632]),
[final] ).
cnf(i_0_3305,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_2029,c_0_1665]),
[final] ).
cnf(i_0_3306,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_2030,c_0_1665]),
[final] ).
cnf(i_0_3307,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_2031,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3308,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(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_2032]),
[final] ).
cnf(i_0_3309,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_2033,c_0_1474]),
[final] ).
cnf(i_0_3310,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2034]),
[final] ).
cnf(i_0_3311,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2035]),
[final] ).
cnf(i_0_3312,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3313,plain,
hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)),
inference(split_conjunct,[status(thm)],[i_0_2037]),
[final] ).
cnf(i_0_3314,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_2038]),
[final] ).
cnf(i_0_3315,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2039]),
[final] ).
cnf(i_0_3316,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_1833]),
[final] ).
cnf(i_0_3317,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_1833]),
[final] ).
cnf(i_0_3318,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_1817]),
[final] ).
cnf(i_0_3319,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_2040]),
[final] ).
cnf(i_0_3320,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)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[i_0_2041,c_0_1632]),
[final] ).
cnf(i_0_3321,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_2042]),
[final] ).
cnf(i_0_3322,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_1960]),
[final] ).
cnf(i_0_3323,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_2043,c_0_1474]),
[final] ).
cnf(i_0_3324,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_2044,c_0_1474]),
[final] ).
cnf(i_0_3325,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_2045,c_0_1474]),
[final] ).
cnf(i_0_3326,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_1955]),
[final] ).
cnf(i_0_3327,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_1968]),
[final] ).
cnf(i_0_3328,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_2046,c_0_1474]),
[final] ).
cnf(i_0_3329,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_2047,c_0_1474]),
[final] ).
cnf(i_0_3330,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_2048,c_0_1474]),
[final] ).
cnf(i_0_3331,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_2049,c_0_1474]),
[final] ).
cnf(i_0_3332,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_1967]),
[final] ).
cnf(i_0_3333,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_2050,c_0_1474]),
[final] ).
cnf(i_0_3334,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_2051,c_0_1474]),
[final] ).
cnf(i_0_3335,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_2052]),
[final] ).
cnf(i_0_3336,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_2053]),
[final] ).
cnf(i_0_3337,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),X3)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_3338,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1943]),
[final] ).
cnf(i_0_3339,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_1973]),
[final] ).
cnf(i_0_3340,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_1974]),
[final] ).
cnf(i_0_3341,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_1975]),
[final] ).
cnf(i_0_3342,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2)),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3343,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_2055]),
[final] ).
cnf(i_0_3344,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_2056]),
[final] ).
cnf(i_0_3345,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_2057]),
[final] ).
cnf(i_0_3346,plain,
( 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3347,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_3348,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2058]),
[final] ).
cnf(i_0_3349,plain,
( c_Int_Onumber__class_Onumber__of(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2059]),
[final] ).
cnf(i_0_3350,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_2060]),
[final] ).
cnf(i_0_3351,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_2061]),
[final] ).
cnf(i_0_3352,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_1477]),
[final] ).
cnf(i_0_3353,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_2062]),
[final] ).
cnf(i_0_3354,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_2063]),
[final] ).
cnf(i_0_3355,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_2064]),
[final] ).
cnf(i_0_3356,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_2065]),
[final] ).
cnf(i_0_3357,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_2066]),
[final] ).
cnf(i_0_3358,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_2067]),
[final] ).
cnf(i_0_3359,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_2068]),
[final] ).
cnf(i_0_3360,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_2069]),
[final] ).
cnf(i_0_3361,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_2070]),
[final] ).
cnf(i_0_3362,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_2071,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3363,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_2072,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3364,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_2073,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3365,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_2074,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3366,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2075]),
[final] ).
cnf(i_0_3367,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2076]),
[final] ).
cnf(i_0_3368,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_3369,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2078]),
[final] ).
cnf(i_0_3370,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2079]),
[final] ).
cnf(i_0_3371,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_3372,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_3373,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2082]),
[final] ).
cnf(i_0_3374,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2083]),
[final] ).
cnf(i_0_3375,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_2084]),
[final] ).
cnf(i_0_3376,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)),
inference(split_conjunct,[status(thm)],[i_0_2085]),
[final] ).
cnf(i_0_3377,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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_3378,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_2087]),
[final] ).
cnf(i_0_3379,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_2088]),
[final] ).
cnf(i_0_3380,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))
| ~ class_Rings_Osemiring__1(X1) ),
inference(rw,[status(thm)],[i_0_2089,c_0_1474]),
[final] ).
cnf(i_0_3381,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_3382,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3383,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_1992]),
[final] ).
cnf(i_0_3384,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_1993]),
[final] ).
cnf(i_0_3385,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_2092]),
[final] ).
cnf(i_0_3386,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_2093]),
[final] ).
cnf(i_0_3387,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_2094]),
[final] ).
cnf(i_0_3388,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_2095]),
[final] ).
cnf(i_0_3389,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_2096]),
[final] ).
cnf(i_0_3390,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_2097]),
[final] ).
cnf(i_0_3391,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_2098]),
[final] ).
cnf(i_0_3392,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_2099]),
[final] ).
cnf(i_0_3393,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_2100]),
[final] ).
cnf(i_0_3394,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),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_2101]),
[final] ).
cnf(i_0_3395,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),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_2102]),
[final] ).
cnf(i_0_3396,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2103]),
[final] ).
cnf(i_0_3397,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3398,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2105]),
[final] ).
cnf(i_0_3399,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_2106,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3400,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2107,c_0_1474]),c_0_1665]),
[final] ).
cnf(i_0_3401,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_2108]),
[final] ).
cnf(i_0_3402,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_2109]),
[final] ).
cnf(i_0_3403,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1318]),
[final] ).
cnf(i_0_3404,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_2108]),
[final] ).
cnf(i_0_3405,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_2110]),
[final] ).
cnf(i_0_3406,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1872]),
[final] ).
cnf(i_0_3407,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_3408,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_2112,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3409,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_2113,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3410,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_Ozero__class_Ozero(tc_Int_Oint),X1)
| epred1_3(X2,X1,X3)
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3411,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_2114]),
[final] ).
cnf(i_0_3412,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_2114]),
[final] ).
cnf(i_0_3413,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2115]),
[final] ).
cnf(i_0_3414,plain,
( c_Orderings_Oord__class_Oless(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3415,plain,
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_3416,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk59_2(X2,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2116]),
[final] ).
cnf(i_0_3417,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_2117]),
[final] ).
cnf(i_0_3418,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_2118]),
[final] ).
cnf(i_0_3419,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_2119]),
[final] ).
cnf(i_0_3420,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_2120]),
[final] ).
cnf(i_0_3421,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X3),hAPP(X2,X4))
| ~ c_SEQ_Oincseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3422,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4),hAPP(X2,X3))
| ~ c_SEQ_Odecseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1864]),
[final] ).
cnf(i_0_3423,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_2121,c_0_1474]),
[final] ).
cnf(i_0_3424,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_3425,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_2123,c_0_1665]),
[final] ).
cnf(i_0_3426,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2124]),
[final] ).
cnf(i_0_3427,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3428,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_3429,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)),X2) = hAPP(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_2127]),
[final] ).
cnf(i_0_3430,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3431,plain,
hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_2129]),
[final] ).
cnf(i_0_3432,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3433,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_2131,c_0_1474]),
[final] ).
cnf(i_0_3434,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_2132,c_0_1474]),
[final] ).
cnf(i_0_3435,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),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_3436,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_1989]),
[final] ).
cnf(i_0_3437,plain,
hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[i_0_2133,c_0_1474]),
[final] ).
cnf(i_0_3438,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
inference(rw,[status(thm)],[i_0_2134,c_0_1474]),
[final] ).
cnf(i_0_3439,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_3440,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_2136,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3441,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_2137,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3442,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_2138,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3443,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_2139,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3444,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,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3445,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_2141]),
[final] ).
cnf(i_0_3446,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk58_1(X1))
| ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2025]),
[final] ).
cnf(i_0_3447,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2142]),
[final] ).
cnf(i_0_3448,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3449,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2143]),
[final] ).
cnf(i_0_3450,plain,
( c_SEQ_Osubseq(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,esk27_1(X1)),hAPP(X1,esk28_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2144]),
[final] ).
cnf(i_0_3451,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)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X1))),
inference(split_conjunct,[status(thm)],[i_0_2145]),
[final] ).
cnf(i_0_3452,plain,
( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_3453,plain,
( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3454,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_2108]),
[final] ).
cnf(i_0_3455,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_2146]),
[final] ).
cnf(i_0_3456,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2147]),
[final] ).
cnf(i_0_3457,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2148]),
[final] ).
cnf(i_0_3458,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3459,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_3460,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2075]),
[final] ).
cnf(i_0_3461,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2076]),
[final] ).
cnf(i_0_3462,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_3463,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2078]),
[final] ).
cnf(i_0_3464,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2079]),
[final] ).
cnf(i_0_3465,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(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_2080]),
[final] ).
cnf(i_0_3466,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_2108]),
[final] ).
cnf(i_0_3467,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_2108]),
[final] ).
cnf(i_0_3468,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_2151,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3469,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_2152]),
[final] ).
cnf(i_0_3470,plain,
c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2153]),
[final] ).
cnf(i_0_3471,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3472,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_2108]),
[final] ).
cnf(i_0_3473,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3))
| ~ c_SEQ_Osubseq(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2144]),
[final] ).
cnf(i_0_3474,plain,
( 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),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2154]),
[final] ).
cnf(i_0_3475,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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2155]),
[final] ).
cnf(i_0_3476,plain,
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_3477,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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2156]),
[final] ).
cnf(i_0_3478,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2157]),
[final] ).
cnf(i_0_3479,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3480,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_2158,c_0_1474]),
[final] ).
cnf(i_0_3481,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1943]),
[final] ).
cnf(i_0_3482,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_2159]),
[final] ).
cnf(i_0_3483,plain,
( hBOOL(hAPP(X1,esk58_1(X1)))
| ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2025]),
[final] ).
cnf(i_0_3484,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 != hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2160]),
[final] ).
cnf(i_0_3485,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2161]),
[final] ).
cnf(i_0_3486,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3487,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3488,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2116]),
[final] ).
cnf(i_0_3489,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk53_2(X2,X1))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3490,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk51_2(X2,X1))
| ~ c_SEQ_OBseq(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1535]),
[final] ).
cnf(i_0_3491,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),esk34_1(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_1335]),
[final] ).
cnf(i_0_3492,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_2165]),
[final] ).
cnf(i_0_3493,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),esk32_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_1780]),
[final] ).
cnf(i_0_3494,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_2166]),
[final] ).
cnf(i_0_3495,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_2166]),
[final] ).
cnf(i_0_3496,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_2167,c_0_1474]),
[final] ).
cnf(i_0_3497,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_2168,c_0_1474]),
[final] ).
cnf(i_0_3498,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_2169]),
[final] ).
cnf(i_0_3499,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2142]),
[final] ).
cnf(i_0_3500,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2143]),
[final] ).
cnf(i_0_3501,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2017]),
[final] ).
cnf(i_0_3502,plain,
( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3503,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_3504,plain,
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2147]),
[final] ).
cnf(i_0_3505,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2148]),
[final] ).
cnf(i_0_3506,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_2170]),
[final] ).
cnf(i_0_3507,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_2171]),
[final] ).
cnf(i_0_3508,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_2172]),
[final] ).
cnf(i_0_3509,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_2173]),
[final] ).
cnf(i_0_3510,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_2174]),
[final] ).
cnf(i_0_3511,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_2175]),
[final] ).
cnf(i_0_3512,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_2176]),
[final] ).
cnf(i_0_3513,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_2177]),
[final] ).
cnf(i_0_3514,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_2178]),
[final] ).
cnf(i_0_3515,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_2179]),
[final] ).
cnf(i_0_3516,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3517,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2017]),
[final] ).
cnf(i_0_3518,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_2181]),
[final] ).
cnf(i_0_3519,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_2182]),
[final] ).
cnf(i_0_3520,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_2183]),
[final] ).
cnf(i_0_3521,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_2184]),
[final] ).
cnf(i_0_3522,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_2185]),
[final] ).
cnf(i_0_3523,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_2186]),
[final] ).
cnf(i_0_3524,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_2187]),
[final] ).
cnf(i_0_3525,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_2188]),
[final] ).
cnf(i_0_3526,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_2189]),
[final] ).
cnf(i_0_3527,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_2146]),
[final] ).
cnf(i_0_3528,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_2190,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3529,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_2191,c_0_1474]),c_0_1474]),
[final] ).
cnf(i_0_3530,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_2192]),
[final] ).
cnf(i_0_3531,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_2193]),
[final] ).
cnf(i_0_3532,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2154]),
[final] ).
cnf(i_0_3533,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_2155]),
[final] ).
cnf(i_0_3534,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2194]),
[final] ).
cnf(i_0_3535,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_2195,c_0_1474]),
[final] ).
cnf(i_0_3536,plain,
c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X2)),
inference(split_conjunct,[status(thm)],[i_0_2196]),
[final] ).
cnf(i_0_3537,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_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3538,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2) = X3
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_3539,plain,
( 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
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3540,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_2199]),
[final] ).
cnf(i_0_3541,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_2200]),
[final] ).
cnf(i_0_3542,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_2201]),
[final] ).
cnf(i_0_3543,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_2202]),
[final] ).
cnf(i_0_3544,plain,
c_Divides_Odiv__class_Odiv(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(rw,[status(thm)],[i_0_2203,c_0_1474]),
[final] ).
cnf(i_0_3545,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_2204]),
[final] ).
cnf(i_0_3546,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_2205]),
[final] ).
cnf(i_0_3547,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_2206]),
[final] ).
cnf(i_0_3548,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_2206]),
[final] ).
cnf(i_0_3549,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_2207,c_0_1474]),
[final] ).
cnf(i_0_3550,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_2208]),
[final] ).
cnf(i_0_3551,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_2209]),
[final] ).
cnf(i_0_3552,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_2210,c_0_1474]),
[final] ).
cnf(i_0_3553,plain,
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(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2211,c_0_1665]),c_0_1632]),
[final] ).
cnf(i_0_3554,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_1955]),
[final] ).
cnf(i_0_3555,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_2212,c_0_1474]),
[final] ).
cnf(i_0_3556,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_2213,c_0_1474]),
[final] ).
cnf(i_0_3557,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk4_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2214]),
[final] ).
cnf(i_0_3558,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk2_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2215]),
[final] ).
cnf(i_0_3559,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk31_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_1749]),
[final] ).
cnf(i_0_3560,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_2216,c_0_1474]),
[final] ).
cnf(i_0_3561,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1396]),
[final] ).
cnf(i_0_3562,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1397]),
[final] ).
cnf(i_0_3563,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1398]),
[final] ).
cnf(i_0_3564,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_3565,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3566,plain,
( hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(X1,esk55_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3567,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2194]),
[final] ).
cnf(i_0_3568,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_2218]),
[final] ).
cnf(i_0_3569,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_2192]),
[final] ).
cnf(i_0_3570,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_2219]),
[final] ).
cnf(i_0_3571,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_2220]),
[final] ).
cnf(i_0_3572,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk55_1(X1))
| hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3573,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_3574,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_2222]),
[final] ).
cnf(i_0_3575,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_2223]),
[final] ).
cnf(i_0_3576,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_2224]),
[final] ).
cnf(i_0_3577,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_2225]),
[final] ).
cnf(i_0_3578,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_2226]),
[final] ).
cnf(i_0_3579,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_1992]),
[final] ).
cnf(i_0_3580,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_1993]),
[final] ).
cnf(i_0_3581,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X2))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2227]),
[final] ).
cnf(i_0_3582,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk23_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_2228,c_0_1474]),
[final] ).
cnf(i_0_3583,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),esk66_1(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_2229]),
[final] ).
cnf(i_0_3584,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_2225]),
[final] ).
cnf(i_0_3585,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_2226]),
[final] ).
cnf(i_0_3586,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_2230]),
[final] ).
cnf(i_0_3587,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_2231]),
[final] ).
cnf(i_0_3588,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_2232]),
[final] ).
cnf(i_0_3589,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_2233]),
[final] ).
cnf(i_0_3590,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_2234]),
[final] ).
cnf(i_0_3591,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_2235]),
[final] ).
cnf(i_0_3592,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_2236]),
[final] ).
cnf(i_0_3593,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_2237]),
[final] ).
cnf(i_0_3594,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_2238]),
[final] ).
cnf(i_0_3595,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_2239]),
[final] ).
cnf(i_0_3596,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_2240]),
[final] ).
cnf(i_0_3597,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_2241]),
[final] ).
cnf(i_0_3598,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_2242]),
[final] ).
cnf(i_0_3599,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_2169]),
[final] ).
cnf(i_0_3600,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_2243]),
[final] ).
cnf(i_0_3601,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_2244]),
[final] ).
cnf(i_0_3602,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_2087]),
[final] ).
cnf(i_0_3603,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_2206]),
[final] ).
cnf(i_0_3604,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_2245]),
[final] ).
cnf(i_0_3605,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_2246]),
[final] ).
cnf(i_0_3606,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3607,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_2241]),
[final] ).
cnf(i_0_3608,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_2242]),
[final] ).
cnf(i_0_3609,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_2248]),
[final] ).
cnf(i_0_3610,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_2146]),
[final] ).
cnf(i_0_3611,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_2249,c_0_1474]),
[final] ).
cnf(i_0_3612,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_2250]),
[final] ).
cnf(i_0_3613,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_2250]),
[final] ).
cnf(i_0_3614,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_2251]),
[final] ).
cnf(i_0_3615,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2252]),
[final] ).
cnf(i_0_3616,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_2253]),
[final] ).
cnf(i_0_3617,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2254]),
[final] ).
cnf(i_0_3618,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2255]),
[final] ).
cnf(i_0_3619,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_2256]),
[final] ).
cnf(i_0_3620,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_2257]),
[final] ).
cnf(i_0_3621,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_2258]),
[final] ).
cnf(i_0_3622,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_2259]),
[final] ).
cnf(i_0_3623,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_2260]),
[final] ).
cnf(i_0_3624,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_2261]),
[final] ).
cnf(i_0_3625,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_2262]),
[final] ).
cnf(i_0_3626,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_2263]),
[final] ).
cnf(i_0_3627,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_3628,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_2265]),
[final] ).
cnf(i_0_3629,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_2257]),
[final] ).
cnf(i_0_3630,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_3631,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[i_0_2267]),
[final] ).
cnf(i_0_3632,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_2214]),
[final] ).
cnf(i_0_3633,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_2215]),
[final] ).
cnf(i_0_3634,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_2258]),
[final] ).
cnf(i_0_3635,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_2259]),
[final] ).
cnf(i_0_3636,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_2260]),
[final] ).
cnf(i_0_3637,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_2261]),
[final] ).
cnf(i_0_3638,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_2262]),
[final] ).
cnf(i_0_3639,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_2268]),
[final] ).
cnf(i_0_3640,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_2269]),
[final] ).
cnf(i_0_3641,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_2270]),
[final] ).
cnf(i_0_3642,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_2271]),
[final] ).
cnf(i_0_3643,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(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_Int_Oint),
inference(rw,[status(thm)],[i_0_2272,c_0_1474]),
[final] ).
cnf(i_0_3644,plain,
hAPP(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_2273,c_0_1474]),
[final] ).
cnf(i_0_3645,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3646,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_2192]),
[final] ).
cnf(i_0_3647,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Oone__class_Oone(X2)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_2274]),
[final] ).
cnf(i_0_3648,plain,
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ epred1_3(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3649,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2275]),
[final] ).
cnf(i_0_3650,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2276]),
[final] ).
cnf(i_0_3651,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk19_2(X1,X2),esk20_2(X1,X2))
| c_SEQ_Omonoseq(X2,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1861]),
[final] ).
cnf(i_0_3652,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk17_2(X1,X2),esk18_2(X1,X2))
| c_SEQ_Omonoseq(X2,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1862]),
[final] ).
cnf(i_0_3653,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk12_2(X1,X2),esk13_2(X1,X2))
| c_SEQ_Omonoseq(X2,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_3654,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk10_2(X1,X2),esk11_2(X1,X2))
| c_SEQ_Omonoseq(X2,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_3655,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk8_2(X1,X2),esk9_2(X1,X2))
| c_SEQ_Oincseq(X2,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3656,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk6_2(X1,X2),esk7_2(X1,X2))
| c_SEQ_Odecseq(X2,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1864]),
[final] ).
cnf(i_0_3657,plain,
( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3658,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(rw,[status(thm)],[i_0_2277,c_0_1474]),
[final] ).
cnf(i_0_3659,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_2278]),
[final] ).
cnf(i_0_3660,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_2278]),
[final] ).
cnf(i_0_3661,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2274]),
[final] ).
cnf(i_0_3662,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_2243]),
[final] ).
cnf(i_0_3663,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3664,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_2279]),
[final] ).
cnf(i_0_3665,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_2280]),
[final] ).
cnf(i_0_3666,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_2281]),
[final] ).
cnf(i_0_3667,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_2282]),
[final] ).
cnf(i_0_3668,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_2283]),
[final] ).
cnf(i_0_3669,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_2284]),
[final] ).
cnf(i_0_3670,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_2182]),
[final] ).
cnf(i_0_3671,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_3672,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2286]),
[final] ).
cnf(i_0_3673,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_2287]),
[final] ).
cnf(i_0_3674,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_2288]),
[final] ).
cnf(i_0_3675,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_2185]),
[final] ).
cnf(i_0_3676,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_2289]),
[final] ).
cnf(i_0_3677,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_2184]),
[final] ).
cnf(i_0_3678,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_2290]),
[final] ).
cnf(i_0_3679,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_2291]),
[final] ).
cnf(i_0_3680,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_2292]),
[final] ).
cnf(i_0_3681,plain,
( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk66_1(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_2229]),
[final] ).
cnf(i_0_3682,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_2293]),
[final] ).
cnf(i_0_3683,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_2294]),
[final] ).
cnf(i_0_3684,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk53_2(X1,X2))
| ~ c_SEQ_OBseq(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3685,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk51_2(X1,X2))
| ~ c_SEQ_OBseq(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1535]),
[final] ).
cnf(i_0_3686,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_2295,c_0_1474]),
[final] ).
cnf(i_0_3687,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_2296]),
[final] ).
cnf(i_0_3688,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_2297,c_0_1474]),
[final] ).
cnf(i_0_3689,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_2298]),
[final] ).
cnf(i_0_3690,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_2299]),
[final] ).
cnf(i_0_3691,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_2300]),
[final] ).
cnf(i_0_3692,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_2301]),
[final] ).
cnf(i_0_3693,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_2302]),
[final] ).
cnf(i_0_3694,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_2303]),
[final] ).
cnf(i_0_3695,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_2304]),
[final] ).
cnf(i_0_3696,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_2305]),
[final] ).
cnf(i_0_3697,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_2306]),
[final] ).
cnf(i_0_3698,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3699,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2308]),
[final] ).
cnf(i_0_3700,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_2309]),
[final] ).
cnf(i_0_3701,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_2310]),
[final] ).
cnf(i_0_3702,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_2311]),
[final] ).
cnf(i_0_3703,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_2312]),
[final] ).
cnf(i_0_3704,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Ozero__class_Ozero(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3705,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_2313]),
[final] ).
cnf(i_0_3706,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_2314]),
[final] ).
cnf(i_0_3707,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_2315]),
[final] ).
cnf(i_0_3708,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_2316]),
[final] ).
cnf(i_0_3709,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oabs__class_Oabs(X2,X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2227]),
[final] ).
cnf(i_0_3710,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_2233]),
[final] ).
cnf(i_0_3711,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_2234]),
[final] ).
cnf(i_0_3712,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_2231]),
[final] ).
cnf(i_0_3713,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_2256]),
[final] ).
cnf(i_0_3714,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3715,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X1))),
inference(split_conjunct,[status(thm)],[i_0_2318]),
[final] ).
cnf(i_0_3716,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_2278]),
[final] ).
cnf(i_0_3717,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3718,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2182]),
[final] ).
cnf(i_0_3719,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_3720,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_3721,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_3722,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_3723,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_3724,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| X2 = X1
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3725,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_3726,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2323]),
[final] ).
cnf(i_0_3727,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Nat__Numeral_Oneg(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2324]),
[final] ).
cnf(i_0_3728,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_2325]),
[final] ).
cnf(i_0_3729,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_2326]),
[final] ).
cnf(i_0_3730,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_2251]),
[final] ).
cnf(i_0_3731,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_2327]),
[final] ).
cnf(i_0_3732,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2254]),
[final] ).
cnf(i_0_3733,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_2255]),
[final] ).
cnf(i_0_3734,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2328]),
[final] ).
cnf(i_0_3735,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_3736,plain,
( c_Nat__Numeral_Oneg(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3737,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_2331]),
[final] ).
cnf(i_0_3738,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_2332,c_0_1474]),
[final] ).
cnf(i_0_3739,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_2333,c_0_1474]),
[final] ).
cnf(i_0_3740,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_2334,c_0_1474]),
[final] ).
cnf(i_0_3741,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_2335,c_0_1474]),
[final] ).
cnf(i_0_3742,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_2336,c_0_1474]),
[final] ).
cnf(i_0_3743,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_2337,c_0_1474]),
[final] ).
cnf(i_0_3744,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_2338]),
[final] ).
cnf(i_0_3745,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_2339]),
[final] ).
cnf(i_0_3746,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_2340]),
[final] ).
cnf(i_0_3747,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(X2,X1)
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3748,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_2341]),
[final] ).
cnf(i_0_3749,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_2341]),
[final] ).
cnf(i_0_3750,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_2342]),
[final] ).
cnf(i_0_3751,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_2343,c_0_1474]),
[final] ).
cnf(i_0_3752,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_2344,c_0_1474]),
[final] ).
cnf(i_0_3753,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2345]),
[final] ).
cnf(i_0_3754,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk63_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_3755,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk61_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_3756,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk69_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_3757,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk68_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1649]),
[final] ).
cnf(i_0_3758,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_2346]),
[final] ).
cnf(i_0_3759,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_2347]),
[final] ).
cnf(i_0_3760,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_2348]),
[final] ).
cnf(i_0_3761,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_2349]),
[final] ).
cnf(i_0_3762,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_2350]),
[final] ).
cnf(i_0_3763,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_2351]),
[final] ).
cnf(i_0_3764,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[i_0_2352]),
[final] ).
cnf(i_0_3765,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[i_0_2353]),
[final] ).
cnf(i_0_3766,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)),
inference(split_conjunct,[status(thm)],[i_0_2354]),
[final] ).
cnf(i_0_3767,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oabs__class_Oabs(X1,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2355]),
[final] ).
cnf(i_0_3768,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2258]),
[final] ).
cnf(i_0_3769,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2260]),
[final] ).
cnf(i_0_3770,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_3771,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2356]),
[final] ).
cnf(i_0_3772,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2357]),
[final] ).
cnf(i_0_3773,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3774,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3775,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(X1)),v_r),
inference(split_conjunct,[status(thm)],[i_0_2358]),
[final] ).
cnf(i_0_3776,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_2347]),
[final] ).
cnf(i_0_3777,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,hAPP(X1,X2))
| ~ c_SEQ_Osubseq(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2359]),
[final] ).
cnf(i_0_3778,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_2360]),
[final] ).
cnf(i_0_3779,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2361]),
[final] ).
cnf(i_0_3780,plain,
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2362]),
[final] ).
cnf(i_0_3781,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X2) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2363]),
[final] ).
cnf(i_0_3782,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2364]),
[final] ).
cnf(i_0_3783,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2275]),
[final] ).
cnf(i_0_3784,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_2365]),
[final] ).
cnf(i_0_3785,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2366]),
[final] ).
cnf(i_0_3786,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2367]),
[final] ).
cnf(i_0_3787,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_2368]),
[final] ).
cnf(i_0_3788,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_2369]),
[final] ).
cnf(i_0_3789,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_2369]),
[final] ).
cnf(i_0_3790,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_2370]),
[final] ).
cnf(i_0_3791,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_2370]),
[final] ).
cnf(i_0_3792,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2361]),
[final] ).
cnf(i_0_3793,plain,
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2362]),
[final] ).
cnf(i_0_3794,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2371]),
[final] ).
cnf(i_0_3795,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(split_conjunct,[status(thm)],[i_0_2372]),
[final] ).
cnf(i_0_3796,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_2373]),
[final] ).
cnf(i_0_3797,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X2)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2374]),
[final] ).
cnf(i_0_3798,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_number__of2]),
[final] ).
cnf(i_0_3799,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_2375]),
[final] ).
cnf(i_0_3800,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_2376]),
[final] ).
cnf(i_0_3801,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_2377]),
[final] ).
cnf(i_0_3802,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_2378]),
[final] ).
cnf(i_0_3803,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_2379]),
[final] ).
cnf(i_0_3804,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_3805,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2323]),
[final] ).
cnf(i_0_3806,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_2311]),
[final] ).
cnf(i_0_3807,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_2312]),
[final] ).
cnf(i_0_3808,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_2380]),
[final] ).
cnf(i_0_3809,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_2381]),
[final] ).
cnf(i_0_3810,plain,
( X2 = X3
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)
| ~ class_Nat_Osemiring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2382]),
[final] ).
cnf(i_0_3811,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_2383]),
[final] ).
cnf(i_0_3812,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_2384]),
[final] ).
cnf(i_0_3813,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_2385]),
[final] ).
cnf(i_0_3814,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_2306]),
[final] ).
cnf(i_0_3815,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_2306]),
[final] ).
cnf(i_0_3816,plain,
( c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2386]),
[final] ).
cnf(i_0_3817,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2387]),
[final] ).
cnf(i_0_3818,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
inference(split_conjunct,[status(thm)],[fact_wr]),
[final] ).
cnf(i_0_3819,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_2316]),
[final] ).
cnf(i_0_3820,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2388]),
[final] ).
cnf(i_0_3821,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk27_1(X1),esk28_1(X1))
| c_SEQ_Osubseq(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2144]),
[final] ).
cnf(i_0_3822,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_2236]),
[final] ).
cnf(i_0_3823,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_2389]),
[final] ).
cnf(i_0_3824,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_2390]),
[final] ).
cnf(i_0_3825,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_2391]),
[final] ).
cnf(i_0_3826,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_2392]),
[final] ).
cnf(i_0_3827,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk62_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_3828,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk67_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_3829,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_1750]),
[final] ).
cnf(i_0_3830,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_2313]),
[final] ).
cnf(i_0_3831,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_2314]),
[final] ).
cnf(i_0_3832,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_2393]),
[final] ).
cnf(i_0_3833,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_2394]),
[final] ).
cnf(i_0_3834,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_2395]),
[final] ).
cnf(i_0_3835,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2396]),
[final] ).
cnf(i_0_3836,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_2397]),
[final] ).
cnf(i_0_3837,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_2398]),
[final] ).
cnf(i_0_3838,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_2399]),
[final] ).
cnf(i_0_3839,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_2400]),
[final] ).
cnf(i_0_3840,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_2341]),
[final] ).
cnf(i_0_3841,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_2401]),
[final] ).
cnf(i_0_3842,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_2402]),
[final] ).
cnf(i_0_3843,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_2403]),
[final] ).
cnf(i_0_3844,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_2404]),
[final] ).
cnf(i_0_3845,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_2405]),
[final] ).
cnf(i_0_3846,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_2406]),
[final] ).
cnf(i_0_3847,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2170]),
[final] ).
cnf(i_0_3848,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2170]),
[final] ).
cnf(i_0_3849,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2407]),
[final] ).
cnf(i_0_3850,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2241]),
[final] ).
cnf(i_0_3851,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_2408]),
[final] ).
cnf(i_0_3852,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_2409]),
[final] ).
cnf(i_0_3853,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Nat__Numeral_Oneg(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3854,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_2410]),
[final] ).
cnf(i_0_3855,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_2411]),
[final] ).
cnf(i_0_3856,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_2331]),
[final] ).
cnf(i_0_3857,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2412]),
[final] ).
cnf(i_0_3858,plain,
c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),
inference(split_conjunct,[status(thm)],[i_0_2413]),
[final] ).
cnf(i_0_3859,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_2414]),
[final] ).
cnf(i_0_3860,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_2415,c_0_1474]),
[final] ).
cnf(i_0_3861,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_2108]),
[final] ).
cnf(i_0_3862,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2416]),
[final] ).
cnf(i_0_3863,plain,
( X2 = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Int_Onumber__class_Onumber__of(X1,X3)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2417]),
[final] ).
cnf(i_0_3864,plain,
( c_Nat__Numeral_Oneg(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_2324]),
[final] ).
cnf(i_0_3865,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_2369]),
[final] ).
cnf(i_0_3866,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_2370]),
[final] ).
cnf(i_0_3867,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_2418]),
[final] ).
cnf(i_0_3868,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_2327]),
[final] ).
cnf(i_0_3869,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_1331]),
[final] ).
cnf(i_0_3870,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2419]),
[final] ).
cnf(i_0_3871,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2420]),
[final] ).
cnf(i_0_3872,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_3873,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_3874,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_3875,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2421]),
[final] ).
cnf(i_0_3876,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_2422]),
[final] ).
cnf(i_0_3877,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2423]),
[final] ).
cnf(i_0_3878,plain,
~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[i_0_2424]),
[final] ).
cnf(i_0_3879,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_2425]),
[final] ).
cnf(i_0_3880,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_2426]),
[final] ).
cnf(i_0_3881,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_2427]),
[final] ).
cnf(i_0_3882,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_2428]),
[final] ).
cnf(i_0_3883,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_2429]),
[final] ).
cnf(i_0_3884,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2259]),
[final] ).
cnf(i_0_3885,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2262]),
[final] ).
cnf(i_0_3886,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_3887,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2430]),
[final] ).
cnf(i_0_3888,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_2431]),
[final] ).
cnf(i_0_3889,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_2432]),
[final] ).
cnf(i_0_3890,plain,
( X1 = X2
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2433]),
[final] ).
cnf(i_0_3891,plain,
( X1 = X2
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2434]),
[final] ).
cnf(i_0_3892,plain,
( X1 = X2
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2435]),
[final] ).
cnf(i_0_3893,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_2436]),
[final] ).
cnf(i_0_3894,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_2437]),
[final] ).
cnf(i_0_3895,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
inference(split_conjunct,[status(thm)],[fact_d_I1_J]),
[final] ).
cnf(i_0_3896,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
inference(split_conjunct,[status(thm)],[fact_rp]),
[final] ).
cnf(i_0_3897,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_1792]),
[final] ).
cnf(i_0_3898,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_1589]),
[final] ).
cnf(i_0_3899,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_2365]),
[final] ).
cnf(i_0_3900,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_2365]),
[final] ).
cnf(i_0_3901,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_2438]),
[final] ).
cnf(i_0_3902,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_2439]),
[final] ).
cnf(i_0_3903,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_2440]),
[final] ).
cnf(i_0_3904,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2441]),
[final] ).
cnf(i_0_3905,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2442]),
[final] ).
cnf(i_0_3906,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2443]),
[final] ).
cnf(i_0_3907,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2444]),
[final] ).
cnf(i_0_3908,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[i_0_2445]),
[final] ).
cnf(i_0_3909,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[i_0_2446]),
[final] ).
cnf(i_0_3910,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_2447]),
[final] ).
cnf(i_0_3911,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[i_0_2448]),
[final] ).
cnf(i_0_3912,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_2449]),
[final] ).
cnf(i_0_3913,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_2450]),
[final] ).
cnf(i_0_3914,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_rel__simps_I19_J]),
[final] ).
cnf(i_0_3915,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_2451]),
[final] ).
cnf(i_0_3916,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_SEQ_Oincseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2452]),
[final] ).
cnf(i_0_3917,plain,
( c_SEQ_Omonoseq(X1,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_SEQ_Odecseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2453]),
[final] ).
cnf(i_0_3918,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X1) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[i_0_2454]),
[final] ).
cnf(i_0_3919,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_2451]),
[final] ).
cnf(i_0_3920,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2455]),
[final] ).
cnf(i_0_3921,plain,
c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),
inference(split_conjunct,[status(thm)],[i_0_2456]),
[final] ).
cnf(i_0_3922,plain,
c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),
inference(split_conjunct,[status(thm)],[i_0_2457]),
[final] ).
cnf(i_0_3923,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_2458]),
[final] ).
cnf(i_0_3924,plain,
~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
inference(split_conjunct,[status(thm)],[i_0_2459]),
[final] ).
cnf(i_0_3925,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2460]),
[final] ).
cnf(i_0_3926,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2461]),
[final] ).
cnf(i_0_3927,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2462]),
[final] ).
cnf(i_0_3928,plain,
c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2463]),
[final] ).
cnf(i_0_3929,plain,
c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2464]),
[final] ).
cnf(i_0_3930,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2465]),
[final] ).
cnf(i_0_3931,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2466]),
[final] ).
cnf(i_0_3932,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2467]),
[final] ).
cnf(i_0_3933,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2468]),
[final] ).
cnf(i_0_3934,plain,
( c_Groups_Oabs__class_Oabs(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2455]),
[final] ).
cnf(i_0_3935,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_2458]),
[final] ).
cnf(i_0_3936,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2469]),
[final] ).
cnf(i_0_3937,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2470]),
[final] ).
cnf(i_0_3938,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_2471]),
[final] ).
cnf(i_0_3939,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_2472]),
[final] ).
cnf(i_0_3940,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2465]),
[final] ).
cnf(i_0_3941,plain,
( hAPP(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_2466]),
[final] ).
cnf(i_0_3942,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[i_0_2473]),
[final] ).
cnf(i_0_3943,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2474]),
[final] ).
cnf(i_0_3944,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2475]),
[final] ).
cnf(i_0_3945,plain,
c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[i_0_2476,c_0_1500]),
[final] ).
cnf(i_0_3946,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__0]),
[final] ).
cnf(i_0_3947,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__1]),
[final] ).
cnf(i_0_3948,plain,
hAPP(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_3949,plain,
hAPP(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_3950,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I1_J]),
[final] ).
cnf(i_0_3951,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]),
[final] ).
cnf(i_0_3952,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_2477]),
[final] ).
cnf(i_0_3953,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_2478]),
[final] ).
cnf(i_0_3954,plain,
c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X1),
inference(split_conjunct,[status(thm)],[i_0_2479]),
[final] ).
cnf(i_0_3955,plain,
c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[i_0_2480]),
[final] ).
cnf(i_0_3956,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2481]),
[final] ).
cnf(i_0_3957,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2482]),
[final] ).
cnf(i_0_3958,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_2483]),
[final] ).
cnf(i_0_3959,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2484]),
[final] ).
cnf(i_0_3960,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2485]),
[final] ).
cnf(i_0_3961,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2486]),
[final] ).
cnf(i_0_3962,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2487]),
[final] ).
cnf(i_0_3963,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2488]),
[final] ).
cnf(i_0_3964,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2489]),
[final] ).
cnf(i_0_3965,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2490]),
[final] ).
cnf(i_0_3966,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2491]),
[final] ).
cnf(i_0_3967,plain,
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2492]),
[final] ).
cnf(i_0_3968,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2493]),
[final] ).
cnf(i_0_3969,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2494]),
[final] ).
cnf(i_0_3970,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2495]),
[final] ).
cnf(i_0_3971,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2496]),
[final] ).
cnf(i_0_3972,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2497]),
[final] ).
cnf(i_0_3973,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2498]),
[final] ).
cnf(i_0_3974,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2499]),
[final] ).
cnf(i_0_3975,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2500]),
[final] ).
cnf(i_0_3976,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2501]),
[final] ).
cnf(i_0_3977,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2502]),
[final] ).
cnf(i_0_3978,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2503]),
[final] ).
cnf(i_0_3979,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2504]),
[final] ).
cnf(i_0_3980,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2505]),
[final] ).
cnf(i_0_3981,plain,
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2506]),
[final] ).
cnf(i_0_3982,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2507]),
[final] ).
cnf(i_0_3983,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2508]),
[final] ).
cnf(i_0_3984,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2509]),
[final] ).
cnf(i_0_3985,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2510]),
[final] ).
cnf(i_0_3986,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2511]),
[final] ).
cnf(i_0_3987,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2512]),
[final] ).
cnf(i_0_3988,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2513]),
[final] ).
cnf(i_0_3989,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2514]),
[final] ).
cnf(i_0_3990,plain,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2515]),
[final] ).
cnf(i_0_3991,plain,
( class_Int_Onumber(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2516]),
[final] ).
cnf(i_0_3992,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2517]),
[final] ).
cnf(i_0_3993,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2518]),
[final] ).
cnf(i_0_3994,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2519]),
[final] ).
cnf(i_0_3995,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2520]),
[final] ).
cnf(i_0_3996,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2521]),
[final] ).
cnf(i_0_3997,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2522]),
[final] ).
cnf(i_0_3998,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2523]),
[final] ).
cnf(i_0_3999,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2524]),
[final] ).
cnf(i_0_4000,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2525]),
[final] ).
cnf(i_0_4001,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2526]),
[final] ).
cnf(i_0_4002,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2527]),
[final] ).
cnf(i_0_4003,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2528]),
[final] ).
cnf(i_0_4004,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2529]),
[final] ).
cnf(i_0_4005,plain,
( class_Rings_Osemiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2530]),
[final] ).
cnf(i_0_4006,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2531]),
[final] ).
cnf(i_0_4007,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2532]),
[final] ).
cnf(i_0_4008,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2533]),
[final] ).
cnf(i_0_4009,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_2534]),
[final] ).
cnf(i_0_4010,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2535]),
[final] ).
cnf(i_0_4011,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2536]),
[final] ).
cnf(i_0_4012,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2537]),
[final] ).
cnf(i_0_4013,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2538]),
[final] ).
cnf(i_0_4014,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2539]),
[final] ).
cnf(i_0_4015,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_2540]),
[final] ).
cnf(i_0_4016,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2541]),
[final] ).
cnf(i_0_4017,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_nat__number__of__Pls]),
[final] ).
cnf(i_0_4018,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_zero__is__num__zero]),
[final] ).
cnf(i_0_4019,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I113_J]),
[final] ).
cnf(i_0_4020,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2542]),
[final] ).
cnf(i_0_4021,plain,
~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_2543]),
[final] ).
cnf(i_0_4022,plain,
~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_2544]),
[final] ).
cnf(i_0_4023,plain,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_expi__zero]),
[final] ).
cnf(i_0_4024,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_4025,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_4026,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_4027,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_4028,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_4029,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_4030,plain,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__def]),
[final] ).
cnf(i_0_4031,plain,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__eq__of__nat]),
[final] ).
cnf(i_0_4032,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_4033,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_4034,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_4035,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_4036,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]),
[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_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]),
[final] ).
cnf(i_0_4039,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_4040,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_4041,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_4042,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_4043,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_4044,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_4045,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]),
[final] ).
cnf(i_0_4046,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
[final] ).
cnf(i_0_4047,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]),
[final] ).
cnf(i_0_4048,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]),
[final] ).
cnf(i_0_4049,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]),
[final] ).
cnf(i_0_4050,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
[final] ).
cnf(i_0_4051,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
[final] ).
cnf(i_0_4052,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_4053,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_4054,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_4055,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_4056,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_4057,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_4058,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4059,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4060,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4061,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4062,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]),
[final] ).
cnf(i_0_4063,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_4064,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Power_Opower]),
[final] ).
cnf(i_0_4065,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_4066,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_4067,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_4068,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_4069,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_4070,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]),
[final] ).
cnf(i_0_4071,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring__abs]),
[final] ).
cnf(i_0_4072,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4073,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4074,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4075,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]),
[final] ).
cnf(i_0_4076,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
[final] ).
cnf(i_0_4077,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]),
[final] ).
cnf(i_0_4078,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]),
[final] ).
cnf(i_0_4079,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
[final] ).
cnf(i_0_4080,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]),
[final] ).
cnf(i_0_4081,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_4082,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_4083,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_4084,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_4085,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_4086,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_4087,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_4088,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_4089,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_4090,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4091,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4092,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4093,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_4094,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]),
[final] ).
cnf(i_0_4095,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_4096,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_4097,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_4098,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_4099,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_4100,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_4101,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_4102,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_4103,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_4104,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_4105,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_4106,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4107,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4108,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4109,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4110,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_4111,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_4112,plain,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_4113,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_4114,plain,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_4115,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_4116,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_4117,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_4118,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_4119,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_4120,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4121,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4122,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4123,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4124,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]),
[final] ).
cnf(i_0_4125,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_4126,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]),
[final] ).
cnf(i_0_4127,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_4128,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_4129,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_4130,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_4131,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_4132,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_4133,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_4134,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_4135,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]),
[final] ).
cnf(i_0_4136,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_4137,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]),
[final] ).
cnf(i_0_4138,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_4139,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_4140,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_4141,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_4142,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_4143,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_4144,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_4145,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]),
[final] ).
cnf(i_0_4146,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]),
[final] ).
cnf(i_0_4147,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_4148,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_4149,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_4150,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber__ring]),
[final] ).
cnf(i_0_4151,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
[final] ).
cnf(i_0_4152,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]),
[final] ).
cnf(i_0_4153,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber]),
[final] ).
cnf(i_0_4154,plain,
class_Int_Onumber(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
[final] ).
cnf(i_0_4155,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]),
[final] ).
cnf(i_0_4156,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
[final] ).
cnf(i_0_4157,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_4158,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_4159,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_4160,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_4161,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_4162,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_4163,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4164,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4165,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4166,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_4167,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_4168,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_4169,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_4170,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_4171,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_4172,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_4173,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_4174,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4175,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4176,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4177,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4178,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_4179,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_4180,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_4181,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_4182,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_4183,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_4184,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_4185,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_4186,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_4187,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_4188,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_4189,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_4190,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_4191,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]),
[final] ).
cnf(i_0_4192,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
[final] ).
cnf(i_0_4193,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]),
[final] ).
cnf(i_0_4194,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]),
[final] ).
cnf(i_0_4195,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_4196,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]),
[final] ).
cnf(i_0_4197,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_4198,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4199,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4200,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4201,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4202,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]),
[final] ).
cnf(i_0_4203,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_4204,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]),
[final] ).
cnf(i_0_4205,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_4206,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_4207,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_4208,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_4209,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_4210,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_4211,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_4212,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_4213,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_4214,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_4215,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_4216,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_4217,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_4218,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_4219,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_4220,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_4221,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_4222,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_4223,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
[final] ).
cnf(i_0_4224,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]),
[final] ).
cnf(i_0_4225,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_4226,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_4227,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
[final] ).
cnf(i_0_4228,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]),
[final] ).
cnf(i_0_4229,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_4230,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_4231,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]),
[final] ).
cnf(i_0_4232,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_4233,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_4234,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_4235,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_4236,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_4237,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_4238,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_4239,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_4240,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
[final] ).
cnf(i_0_4241,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]),
[final] ).
cnf(i_0_4242,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_4243,plain,
c_SEQ_Osubseq(v_f____),
inference(split_conjunct,[status(thm)],[fact_fz_I1_J]),
[final] ).
cnf(i_0_4244,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]),
[final] ).
cnf(i_0_4245,axiom,
X1 = X1 ).
cnf(i_0_4246,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4247,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4248,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_4249,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_4250,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_4251,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_4252,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_4253,axiom,
( X1 != X2
| c_RealDef_Oreal(X1) = c_RealDef_Oreal(X2) ) ).
cnf(i_0_4254,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_4255,axiom,
( X1 != X2
| c_Complex_Orcis(X1,X3) = c_Complex_Orcis(X2,X3) ) ).
cnf(i_0_4256,axiom,
( X1 != X2
| c_Complex_Orcis(X3,X1) = c_Complex_Orcis(X3,X2) ) ).
cnf(i_0_4257,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_4258,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_4259,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).
cnf(i_0_4260,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_4261,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_4262,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_4263,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_4264,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_4265,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_4266,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4267,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_4268,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_4269,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_4270,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_4271,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_4272,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_4273,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_4274,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_4275,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,X4,X5) ) ).
cnf(i_0_4276,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X1,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X2,X4,X5) ) ).
cnf(i_0_4277,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X1,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X2,X5) ) ).
cnf(i_0_4278,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X2) ) ).
cnf(i_0_4279,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_4280,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_4281,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Rings_Oinverse__class_Odivide(X2,X3,X4) ) ).
cnf(i_0_4282,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X1,X4) = c_Rings_Oinverse__class_Odivide(X3,X2,X4) ) ).
cnf(i_0_4283,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X4,X1) = c_Rings_Oinverse__class_Odivide(X3,X4,X2) ) ).
cnf(i_0_4284,axiom,
( X1 != X2
| esk72_2(X1,X3) = esk72_2(X2,X3) ) ).
cnf(i_0_4285,axiom,
( X1 != X2
| esk72_2(X3,X1) = esk72_2(X3,X2) ) ).
cnf(i_0_4286,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_4287,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_4288,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_4289,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_4290,axiom,
( X1 != X2
| c_Complex_Oexpi(X1) = c_Complex_Oexpi(X2) ) ).
cnf(i_0_4291,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4292,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4293,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4294,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4295,axiom,
( X1 != X2
| ~ c_SEQ_OBseq(X1,X3)
| c_SEQ_OBseq(X2,X3) ) ).
cnf(i_0_4296,axiom,
( X1 != X2
| ~ c_SEQ_OBseq(X3,X1)
| c_SEQ_OBseq(X3,X2) ) ).
cnf(i_0_4297,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4298,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4299,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4300,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4301,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_4302,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_4303,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_4304,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4305,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4306,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4307,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4308,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4309,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4310,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4311,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4312,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4313,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4314,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_4315,axiom,
( X1 != X2
| ~ c_SEQ_Omonoseq(X1,X3)
| c_SEQ_Omonoseq(X2,X3) ) ).
cnf(i_0_4316,axiom,
( X1 != X2
| ~ c_SEQ_Omonoseq(X3,X1)
| c_SEQ_Omonoseq(X3,X2) ) ).
cnf(i_0_4317,axiom,
( X1 != X2
| ~ c_SEQ_Oincseq(X1,X3)
| c_SEQ_Oincseq(X2,X3) ) ).
cnf(i_0_4318,axiom,
( X1 != X2
| ~ c_SEQ_Oincseq(X3,X1)
| c_SEQ_Oincseq(X3,X2) ) ).
cnf(i_0_4319,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_4320,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_4321,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4322,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4323,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4324,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4325,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4326,axiom,
( X1 != X2
| ~ c_SEQ_Osubseq(X1)
| c_SEQ_Osubseq(X2) ) ).
cnf(i_0_4327,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4328,axiom,
( X1 != X2
| ~ c_Nat__Numeral_Oneg(X1)
| c_Nat__Numeral_Oneg(X2) ) ).
cnf(i_0_4329,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4330,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_4331,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4332,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4333,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4334,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4335,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4336,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4337,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4338,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4339,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4340,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_4341,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4342,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4343,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4344,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4345,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4346,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1,X3)
| c_SEQ_Odecseq(X2,X3) ) ).
cnf(i_0_4347,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X3,X1)
| c_SEQ_Odecseq(X3,X2) ) ).
cnf(i_0_4348,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4349,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4350,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4351,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4352,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4353,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4354,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4355,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4356,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4357,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4358,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4359,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4360,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4361,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4362,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4363,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4364,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_4365,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4366,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4367,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4368,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4369,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4370,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4371,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4372,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4373,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4374,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4375,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_4376,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4245_001,axiom,
X1 = X1 ).
cnf(i_0_4246_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4247_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4248_004,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_4249_005,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_4250_006,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_4251_007,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_4252_008,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_4253_009,axiom,
( X1 != X2
| c_RealDef_Oreal(X1) = c_RealDef_Oreal(X2) ) ).
cnf(i_0_4254_010,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_4255_011,axiom,
( X1 != X2
| c_Complex_Orcis(X1,X3) = c_Complex_Orcis(X2,X3) ) ).
cnf(i_0_4256_012,axiom,
( X1 != X2
| c_Complex_Orcis(X3,X1) = c_Complex_Orcis(X3,X2) ) ).
cnf(i_0_4257_013,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_4258_014,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_4259_015,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).
cnf(i_0_4260_016,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_4261_017,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_4262_018,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_4263_019,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_4264_020,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_4265_021,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_4266_022,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4267_023,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_4268_024,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_4269_025,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_4270_026,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_4271_027,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_4272_028,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_4273_029,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_4274_030,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_4275_031,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,X4,X5) ) ).
cnf(i_0_4276_032,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X1,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X2,X4,X5) ) ).
cnf(i_0_4277_033,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X1,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X2,X5) ) ).
cnf(i_0_4278_034,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X2) ) ).
cnf(i_0_4279_035,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_4280_036,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_4281_037,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Rings_Oinverse__class_Odivide(X2,X3,X4) ) ).
cnf(i_0_4282_038,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X1,X4) = c_Rings_Oinverse__class_Odivide(X3,X2,X4) ) ).
cnf(i_0_4283_039,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X4,X1) = c_Rings_Oinverse__class_Odivide(X3,X4,X2) ) ).
cnf(i_0_4284_040,axiom,
( X1 != X2
| esk72_2(X1,X3) = esk72_2(X2,X3) ) ).
cnf(i_0_4285_041,axiom,
( X1 != X2
| esk72_2(X3,X1) = esk72_2(X3,X2) ) ).
cnf(i_0_4286_042,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_4287_043,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_4288_044,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_4289_045,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_4290_046,axiom,
( X1 != X2
| c_Complex_Oexpi(X1) = c_Complex_Oexpi(X2) ) ).
cnf(i_0_4291_047,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4292_048,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4293_049,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4294_050,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4295_051,axiom,
( X1 != X2
| ~ c_SEQ_OBseq(X1,X3)
| c_SEQ_OBseq(X2,X3) ) ).
cnf(i_0_4296_052,axiom,
( X1 != X2
| ~ c_SEQ_OBseq(X3,X1)
| c_SEQ_OBseq(X3,X2) ) ).
cnf(i_0_4297_053,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4298_054,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4299_055,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4300_056,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4301_057,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_4302_058,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_4303_059,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_4304_060,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4305_061,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4306_062,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4307_063,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4308_064,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4309_065,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4310_066,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4311_067,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4312_068,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4313_069,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4314_070,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_4315_071,axiom,
( X1 != X2
| ~ c_SEQ_Omonoseq(X1,X3)
| c_SEQ_Omonoseq(X2,X3) ) ).
cnf(i_0_4316_072,axiom,
( X1 != X2
| ~ c_SEQ_Omonoseq(X3,X1)
| c_SEQ_Omonoseq(X3,X2) ) ).
cnf(i_0_4317_073,axiom,
( X1 != X2
| ~ c_SEQ_Oincseq(X1,X3)
| c_SEQ_Oincseq(X2,X3) ) ).
cnf(i_0_4318_074,axiom,
( X1 != X2
| ~ c_SEQ_Oincseq(X3,X1)
| c_SEQ_Oincseq(X3,X2) ) ).
cnf(i_0_4319_075,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_4320_076,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_4321_077,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4322_078,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4323_079,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4324_080,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4325_081,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4326_082,axiom,
( X1 != X2
| ~ c_SEQ_Osubseq(X1)
| c_SEQ_Osubseq(X2) ) ).
cnf(i_0_4327_083,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4328_084,axiom,
( X1 != X2
| ~ c_Nat__Numeral_Oneg(X1)
| c_Nat__Numeral_Oneg(X2) ) ).
cnf(i_0_4329_085,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4330_086,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_4331_087,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4332_088,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4333_089,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4334_090,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4335_091,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4336_092,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4337_093,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4338_094,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4339_095,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4340_096,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_4341_097,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4342_098,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4343_099,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4344_100,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4345_101,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4346_102,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1,X3)
| c_SEQ_Odecseq(X2,X3) ) ).
cnf(i_0_4347_103,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X3,X1)
| c_SEQ_Odecseq(X3,X2) ) ).
cnf(i_0_4348_104,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4349_105,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4350_106,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4351_107,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4352_108,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4353_109,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4354_110,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4355_111,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4356_112,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4357_113,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4358_114,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4359_115,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4360_116,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4361_117,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4362_118,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4363_119,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4364_120,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_4365_121,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4366_122,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4367_123,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4368_124,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4369_125,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4370_126,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4371_127,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4372_128,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4373_129,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4374_130,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4375_131,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_4376_132,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4377,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,[],[2584]) ).
cnf(i_0_4378,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,[],[2585]) ).
cnf(i_0_4379,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,[],[2598]) ).
cnf(i_0_4380,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,[],[2599]) ).
cnf(i_0_4381,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,[],[2600]) ).
cnf(i_0_4382,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,[],[2601]) ).
cnf(i_0_4383,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,[],[2610]) ).
cnf(i_0_4384,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,[],[2611]) ).
cnf(i_0_4385,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,[],[2612]) ).
cnf(i_0_4386,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,[],[2613]) ).
cnf(i_0_4387,plain,
X1 = X1,
inference(equality_inference,[],[2640]) ).
cnf(i_0_4388,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X3
| X4 = X4 ),
inference(equality_inference,[],[2645]) ).
cnf(i_0_4389,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X3,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),X2),X4),X1),X2))) ),
inference(equality_inference,[],[2671]) ).
cnf(i_0_4390,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,[],[2672]) ).
cnf(i_0_4391,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1),X2) = X3
| 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__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(equality_inference,[],[2722]) ).
cnf(i_0_4392,plain,
( ~ epred1_3(X1,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| ~ 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),X4)
| hBOOL(hAPP(X1,X3)) ),
inference(equality_inference,[],[2732]) ).
cnf(i_0_4393,plain,
( ~ epred1_3(X1,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,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,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(X1,X3)) ),
inference(equality_inference,[],[2733]) ).
cnf(i_0_4394,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1),X2) = X3
| X2 = 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,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(equality_inference,[],[2775]) ).
cnf(i_0_4395,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,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(equality_inference,[],[2786]) ).
cnf(i_0_4396,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(equality_inference,[],[2796]) ).
cnf(i_0_4397,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,[],[2809]) ).
cnf(i_0_4398,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3),X2),X1) = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(equality_inference,[],[2822]) ).
cnf(i_0_4399,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,[],[2849]) ).
cnf(i_0_4400,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,[],[2885]) ).
cnf(i_0_4401,plain,
( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(equality_inference,[],[2965]) ).
cnf(i_0_4402,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)) ),
inference(equality_inference,[],[3013]) ).
cnf(i_0_4403,plain,
( X1 = esk72_2(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2),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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(equality_inference,[],[3079]) ).
cnf(i_0_4404,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,[],[3129]) ).
cnf(i_0_4405,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,[],[3130]) ).
cnf(i_0_4406,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),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1)),X2) ),
inference(equality_inference,[],[3190]) ).
cnf(i_0_4407,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,[],[3216]) ).
cnf(i_0_4408,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(equality_inference,[],[3225]) ).
cnf(i_0_4409,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,[],[3233]) ).
cnf(i_0_4410,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,[],[3234]) ).
cnf(i_0_4411,plain,
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3254]) ).
cnf(i_0_4412,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(equality_inference,[],[3270]) ).
cnf(i_0_4413,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[3342]) ).
cnf(i_0_4414,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[3347]) ).
cnf(i_0_4415,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,[],[3362]) ).
cnf(i_0_4416,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,[],[3363]) ).
cnf(i_0_4417,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,[],[3364]) ).
cnf(i_0_4418,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,[],[3365]) ).
cnf(i_0_4419,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,[],[3378]) ).
cnf(i_0_4420,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(equality_inference,[],[3379]) ).
cnf(i_0_4421,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,[],[3411]) ).
cnf(i_0_4422,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,[],[3412]) ).
cnf(i_0_4423,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,[],[3468]) ).
cnf(i_0_4424,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))),
inference(equality_inference,[],[3488]) ).
cnf(i_0_4425,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,[],[3496]) ).
cnf(i_0_4426,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,[],[3497]) ).
cnf(i_0_4427,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[3512]) ).
cnf(i_0_4428,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[3513]) ).
cnf(i_0_4429,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[3515]) ).
cnf(i_0_4430,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,[],[3549]) ).
cnf(i_0_4431,plain,
X1 = X1,
inference(equality_inference,[],[3550]) ).
cnf(i_0_4432,plain,
X1 = X1,
inference(equality_inference,[],[3551]) ).
cnf(i_0_4433,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,[],[3554]) ).
cnf(i_0_4434,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,[],[3555]) ).
cnf(i_0_4435,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(equality_inference,[],[3565]) ).
cnf(i_0_4436,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,[],[3580]) ).
cnf(i_0_4437,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1))) ),
inference(equality_inference,[],[3581]) ).
cnf(i_0_4438,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3586]) ).
cnf(i_0_4439,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3587]) ).
cnf(i_0_4440,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3588]) ).
cnf(i_0_4441,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3590]) ).
cnf(i_0_4442,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,[],[3611]) ).
cnf(i_0_4443,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,[],[3614]) ).
cnf(i_0_4444,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(equality_inference,[],[3633]) ).
cnf(i_0_4445,plain,
( ~ epred1_3(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(equality_inference,[],[3648]) ).
cnf(i_0_4446,plain,
X1 = X1,
inference(equality_inference,[],[3650]) ).
cnf(i_0_4447,plain,
( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(equality_inference,[],[3657]) ).
cnf(i_0_4448,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,[],[3662]) ).
cnf(i_0_4449,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,[],[3688]) ).
cnf(i_0_4450,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[3704]) ).
cnf(i_0_4451,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,[],[3711]) ).
cnf(i_0_4452,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,[],[3712]) ).
cnf(i_0_4453,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,[],[3713]) ).
cnf(i_0_4454,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,[],[3716]) ).
cnf(i_0_4455,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3719]) ).
cnf(i_0_4456,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3721]) ).
cnf(i_0_4457,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3722]) ).
cnf(i_0_4458,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3723]) ).
cnf(i_0_4459,plain,
( X1 = X1
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(equality_inference,[],[3724]) ).
cnf(i_0_4460,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_inference,[],[3732]) ).
cnf(i_0_4461,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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,[],[3733]) ).
cnf(i_0_4462,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3750]) ).
cnf(i_0_4463,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_inference,[],[3768]) ).
cnf(i_0_4464,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3769]) ).
cnf(i_0_4465,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3773]) ).
cnf(i_0_4466,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3774]) ).
cnf(i_0_4467,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(equality_inference,[],[3783]) ).
cnf(i_0_4468,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,[],[3806]) ).
cnf(i_0_4469,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,[],[3807]) ).
cnf(i_0_4470,plain,
( ~ class_Nat_Osemiring__char__0(X1)
| X2 = X2 ),
inference(equality_inference,[],[3810]) ).
cnf(i_0_4471,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,[],[3814]) ).
cnf(i_0_4472,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,[],[3815]) ).
cnf(i_0_4473,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,[],[3819]) ).
cnf(i_0_4474,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,[],[3829]) ).
cnf(i_0_4475,plain,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3830]) ).
cnf(i_0_4476,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3831]) ).
cnf(i_0_4477,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3848]) ).
cnf(i_0_4478,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3849]) ).
cnf(i_0_4479,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3850]) ).
cnf(i_0_4480,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,[],[3861]) ).
cnf(i_0_4481,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 = X2 ),
inference(equality_inference,[],[3863]) ).
cnf(i_0_4482,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(equality_inference,[],[3869]) ).
cnf(i_0_4483,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3884]) ).
cnf(i_0_4484,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3887]) ).
cnf(i_0_4485,plain,
X1 = X1,
inference(equality_inference,[],[3891]) ).
cnf(i_0_4486,plain,
X1 = X1,
inference(equality_inference,[],[3892]) ).
cnf(i_0_4487,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,[],[3897]) ).
cnf(i_0_4488,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,[],[3899]) ).
cnf(i_0_4489,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,[],[3900]) ).
cnf(i_0_4490,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,[],[3919]) ).
cnf(i_0_4491,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3934]) ).
cnf(i_0_4492,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,[],[3935]) ).
cnf(i_0_4493,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(equality_inference,[],[3940]) ).
cnf(i_0_4494,plain,
hAPP(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,[],[3941]) ).
cnf(i_0_4495,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,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2551,i_0_3465]) ).
cnf(i_0_4496,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3465]) ).
cnf(i_0_4497,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_2551,i_0_3308,i_0_3465,i_0_3636]) ).
cnf(i_0_4498,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_3636]) ).
cnf(i_0_4499,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2551,i_0_3308,i_0_3465,i_0_3636,i_0_3693]) ).
cnf(i_0_4500,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_3693]) ).
cnf(i_0_4501,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2551,i_0_3308,i_0_3465,i_0_3636,i_0_3693,i_0_3884]) ).
cnf(i_0_4502,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3884]) ).
cnf(i_0_4503,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(scs_inference,[],[i_0_2551,i_0_4020,i_0_3308,i_0_3465,i_0_3636,i_0_3693,i_0_3884,i_0_2796]) ).
cnf(i_0_4504,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
inference(rename_variables,[],[i_0_4020]) ).
cnf(i_0_4505,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(rename_variables,[],[i_0_2796]) ).
cnf(i_0_4506,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_2551,i_0_4020,i_0_3308,i_0_3027,i_0_3465,i_0_3636,i_0_3693,i_0_3884,i_0_2796,i_0_2868]) ).
cnf(i_0_4507,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_3027]) ).
cnf(i_0_4508,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_2868]) ).
cnf(i_0_4509,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_2551,i_0_4020,i_0_3715,i_0_3308,i_0_3027,i_0_3465,i_0_3636,i_0_3693,i_0_3884,i_0_2796,i_0_2868,i_0_2878]) ).
cnf(i_0_4510,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X1))),
inference(rename_variables,[],[i_0_3715]) ).
cnf(i_0_4511,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_2878]) ).
cnf(i_0_4512,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1))),
inference(scs_inference,[],[i_0_2551,i_0_4020,i_0_3715,i_0_3308,i_0_3027,i_0_3465,i_0_3636,i_0_3693,i_0_3884,i_0_2796,i_0_2868,i_0_2878,i_0_2879]) ).
cnf(i_0_4513,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rename_variables,[],[i_0_3308]) ).
cnf(i_0_4514,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(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_2879]) ).
cnf(i_0_4515,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_2551,i_0_3906,i_0_4020,i_0_3715,i_0_3308,i_0_3027,i_0_3465,i_0_3636,i_0_3693,i_0_3884,i_0_2796,i_0_2868,i_0_2878,i_0_2879,i_0_2985]) ).
cnf(i_0_4516,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3906]) ).
cnf(i_0_4517,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_2985]) ).
cnf(i_0_4518,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_2551,i_0_3906,i_0_4020,i_0_3715,i_0_3560,i_0_3308,i_0_3027,i_0_3465,i_0_3636,i_0_3693,i_0_3884,i_0_2796,i_0_2868,i_0_2878,i_0_2879,i_0_2985,i_0_2986]) ).
cnf(i_0_4519,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_3560]) ).
cnf(i_0_4520,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_2986]) ).
cnf(i_0_4521,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_2551,i_0_3906,i_0_4516,i_0_4020,i_0_3715,i_0_3560,i_0_3308,i_0_3027,i_0_3465,i_0_3636,i_0_3693,i_0_3884,i_0_2796,i_0_2868,i_0_2878,i_0_2879,i_0_2985,i_0_2986,i_0_2987]) ).
cnf(i_0_4522,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3906]) ).
cnf(i_0_4523,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_2987]) ).
cnf(i_0_4524,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(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_2551,i_0_3906,i_0_4516,i_0_4522,i_0_4020,i_0_3715,i_0_3560,i_0_3308,i_0_3027,i_0_3465,i_0_3636,i_0_3693,i_0_3884,i_0_2796,i_0_2868,i_0_2878,i_0_2879,i_0_2985,i_0_2986,i_0_2987,i_0_3074]) ).
cnf(i_0_4525,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3906]) ).
cnf(i_0_4526,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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)) ),
inference(rename_variables,[],[i_0_3074]) ).
cnf(i_0_4527,plain,
$false,
inference(scs_inference,[],[i_0_2551,i_0_3906,i_0_4516,i_0_4522,i_0_4020,i_0_3715,i_0_3029,i_0_3560,i_0_3308,i_0_3027,i_0_3465,i_0_3636,i_0_3693,i_0_3884,i_0_2796,i_0_2868,i_0_2878,i_0_2879,i_0_2985,i_0_2986,i_0_2987,i_0_3074,i_0_3106]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW225+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 06:28:05 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 6.22/5.80 % Version : CSE_E---1.7
% 6.22/5.80 % Problem : theBenchmark.p
% 6.22/5.80 % SZS status Theorem for theBenchmark.p
% 6.22/5.80 % SZS output start CNFRefutation
% See solution above
% 6.42/5.99 % Total time : 5.451s
%------------------------------------------------------------------------------